\[x + y \cdot \frac{z - t}{z - a}\]

↓

\[\mathsf{fma}\left(y, \left(z - t\right) \cdot \frac{1}{z - a}, x\right)\]

x + y \cdot \frac{z - t}{z - a}

↓

\mathsf{fma}\left(y, \left(z - t\right) \cdot \frac{1}{z - a}, x\right)

double f(double x, double y, double z, double t, double a) {
        double r552699 = x;
        double r552700 = y;
        double r552701 = z;
        double r552702 = t;
        double r552703 = r552701 - r552702;
        double r552704 = a;
        double r552705 = r552701 - r552704;
        double r552706 = r552703 / r552705;
        double r552707 = r552700 * r552706;
        double r552708 = r552699 + r552707;
        return r552708;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r552709 = y;
        double r552710 = z;
        double r552711 = t;
        double r552712 = r552710 - r552711;
        double r552713 = 1.0;
        double r552714 = a;
        double r552715 = r552710 - r552714;
        double r552716 = r552713 / r552715;
        double r552717 = r552712 * r552716;
        double r552718 = x;
        double r552719 = fma(r552709, r552717, r552718);
        return r552719;
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Original	1.4
Target	1.3
Herbie	1.5

Derivation

Initial program 1.4
\[x + y \cdot \frac{z - t}{z - a}\]
Simplified1.4
\[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{z - a}, x\right)}\]
Using strategy rm
Applied div-inv1.5
\[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(z - t\right) \cdot \frac{1}{z - a}}, x\right)\]
Final simplification1.5
\[\leadsto \mathsf{fma}\left(y, \left(z - t\right) \cdot \frac{1}{z - a}, x\right)\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (* y (/ (- z t) (- z a)))))

Error

Target

Derivation

Reproduce