Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B

Average Error: 6.1 → 6.1

Time: 19.9s

Precision: 64

Math

\[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]

↓

\[\mathsf{fma}\left(y \cdot 4, t - z \cdot z, x \cdot x\right)\]

C

double f(double x, double y, double z, double t) {
        double r461353 = x;
        double r461354 = r461353 * r461353;
        double r461355 = y;
        double r461356 = 4.0;
        double r461357 = r461355 * r461356;
        double r461358 = z;
        double r461359 = r461358 * r461358;
        double r461360 = t;
        double r461361 = r461359 - r461360;
        double r461362 = r461357 * r461361;
        double r461363 = r461354 - r461362;
        return r461363;
}

↓

double f(double x, double y, double z, double t) {
        double r461364 = y;
        double r461365 = 4.0;
        double r461366 = r461364 * r461365;
        double r461367 = t;
        double r461368 = z;
        double r461369 = r461368 * r461368;
        double r461370 = r461367 - r461369;
        double r461371 = x;
        double r461372 = r461371 * r461371;
        double r461373 = fma(r461366, r461370, r461372);
        return r461373;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.1
Target	6.1
Herbie	6.1

\[x \cdot x - 4 \cdot \left(y \cdot \left(z \cdot z - t\right)\right)\]

Derivation

1. Initial program 6.1

   \[x \cdot x - \left(y \cdot 4\right) \cdot \left(z \cdot z - t\right)\]

2. Simplified 6.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot 4, t - z \cdot z, x \cdot x\right)}\]

3. Final simplification 6.1

   \[\leadsto \mathsf{fma}\left(y \cdot 4, t - z \cdot z, x \cdot x\right)\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, B"

  :herbie-target
  (- (* x x) (* 4.0 (* y (- (* z z) t))))

  (- (* x x) (* (* y 4.0) (- (* z z) t))))