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

Average Error: 10.6 → 1.3

Time: 25.0s

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 r373823 = x;
        double r373824 = y;
        double r373825 = z;
        double r373826 = t;
        double r373827 = r373825 - r373826;
        double r373828 = r373824 * r373827;
        double r373829 = a;
        double r373830 = r373825 - r373829;
        double r373831 = r373828 / r373830;
        double r373832 = r373823 + r373831;
        return r373832;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r373833 = z;
        double r373834 = t;
        double r373835 = r373833 - r373834;
        double r373836 = a;
        double r373837 = r373833 - r373836;
        double r373838 = r373835 / r373837;
        double r373839 = y;
        double r373840 = x;
        double r373841 = fma(r373838, r373839, r373840);
        return r373841;
}

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))))