Learning goal: in a convergent regime, a log–log step-error plot can be approximately linear. Its slope reflects numerical order, and its height reflects a problem-dependent error scale. Velocity variation, field regularity, and error propagation all matter.

Log step count versus median distance to a 512-step Heun reference; dashed: slopes −1 and −2.
Integrate only to t=0.9: near the endpoint, σ _t approaches zero and steep behavior can obscure the tested convergence regime.

In solver mode, the curves can have different slopes: Euler is about −1.05 and Heun about −2.05 in this run. Those correspond to first- and second-order regimes, subject to reference and finite-range error. In path mode, slopes can be similar because both use Euler, while heights differ. This toy's linear path has a larger measured error scale by about two to three times. Compare slopes and scales, rather than only one score at one step count.