Average Error: 1.3 → 1.3
Time: 21.0s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)\]
x + y \cdot \frac{z - t}{z - a}
↓
\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)
double f(double x, double y, double z, double t, double a) {
        double r19064930 = x;
        double r19064931 = y;
        double r19064932 = z;
        double r19064933 = t;
        double r19064934 = r19064932 - r19064933;
        double r19064935 = a;
        double r19064936 = r19064932 - r19064935;
        double r19064937 = r19064934 / r19064936;
        double r19064938 = r19064931 * r19064937;
        double r19064939 = r19064930 + r19064938;
        return r19064939;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r19064940 = z;
        double r19064941 = t;
        double r19064942 = r19064940 - r19064941;
        double r19064943 = a;
        double r19064944 = r19064940 - r19064943;
        double r19064945 = r19064942 / r19064944;
        double r19064946 = y;
        double r19064947 = x;
        double r19064948 = fma(r19064945, r19064946, r19064947);
        return r19064948;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original1.3
Target1.1
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  2. Simplified1.3

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)}\]

  3. Final simplification1.3

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

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

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