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

Average Error: 10.6 → 1.3

Time: 20.8s

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 r23602670 = x;
        double r23602671 = y;
        double r23602672 = z;
        double r23602673 = t;
        double r23602674 = r23602672 - r23602673;
        double r23602675 = r23602671 * r23602674;
        double r23602676 = a;
        double r23602677 = r23602672 - r23602676;
        double r23602678 = r23602675 / r23602677;
        double r23602679 = r23602670 + r23602678;
        return r23602679;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r23602680 = z;
        double r23602681 = t;
        double r23602682 = r23602680 - r23602681;
        double r23602683 = a;
        double r23602684 = r23602680 - r23602683;
        double r23602685 = r23602682 / r23602684;
        double r23602686 = y;
        double r23602687 = x;
        double r23602688 = fma(r23602685, r23602686, r23602687);
        return r23602688;
}

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	1.3
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 2019172 +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))))