Average Error: 1.3 → 1.3
Time: 27.2s
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 r23602807 = x;
        double r23602808 = y;
        double r23602809 = z;
        double r23602810 = t;
        double r23602811 = r23602809 - r23602810;
        double r23602812 = a;
        double r23602813 = r23602809 - r23602812;
        double r23602814 = r23602811 / r23602813;
        double r23602815 = r23602808 * r23602814;
        double r23602816 = r23602807 + r23602815;
        return r23602816;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r23602817 = z;
        double r23602818 = t;
        double r23602819 = r23602817 - r23602818;
        double r23602820 = a;
        double r23602821 = r23602817 - r23602820;
        double r23602822 = r23602819 / r23602821;
        double r23602823 = y;
        double r23602824 = x;
        double r23602825 = fma(r23602822, r23602823, r23602824);
        return r23602825;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original1.3
Target1.3
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 2019172 +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)))))