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

Average Error: 11.0 → 1.3

Time: 23.8s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r457215 = x;
        double r457216 = y;
        double r457217 = z;
        double r457218 = t;
        double r457219 = r457217 - r457218;
        double r457220 = r457216 * r457219;
        double r457221 = a;
        double r457222 = r457221 - r457218;
        double r457223 = r457220 / r457222;
        double r457224 = r457215 + r457223;
        return r457224;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r457225 = y;
        double r457226 = z;
        double r457227 = t;
        double r457228 = r457226 - r457227;
        double r457229 = a;
        double r457230 = r457229 - r457227;
        double r457231 = r457228 / r457230;
        double r457232 = x;
        double r457233 = fma(r457225, r457231, r457232);
        return r457233;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	11.0
Target	1.2
Herbie	1.3

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

Derivation

1. Initial program 11.0

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

2. Simplified 1.3

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

3. Final simplification 1.3

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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