Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Average Error: 10.6 → 1.3

Time: 21.7s

Precision: 64

Math

\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r24404091 = x;
        double r24404092 = y;
        double r24404093 = z;
        double r24404094 = t;
        double r24404095 = r24404093 - r24404094;
        double r24404096 = r24404092 * r24404095;
        double r24404097 = a;
        double r24404098 = r24404093 - r24404097;
        double r24404099 = r24404096 / r24404098;
        double r24404100 = r24404091 + r24404099;
        return r24404100;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r24404101 = z;
        double r24404102 = t;
        double r24404103 = r24404101 - r24404102;
        double r24404104 = a;
        double r24404105 = r24404101 - r24404104;
        double r24404106 = r24404103 / r24404105;
        double r24404107 = y;
        double r24404108 = x;
        double r24404109 = fma(r24404106, r24404107, r24404108);
        return r24404109;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.6
Target	1.2
Herbie	1.3

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

Derivation

1. Initial program 10.6

   \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]

2. Simplified 1.3

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

3. Final simplification 1.3

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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