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

Average Error: 6.1 → 6.1

Time: 22.1s

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 r436130 = x;
        double r436131 = r436130 * r436130;
        double r436132 = y;
        double r436133 = 4.0;
        double r436134 = r436132 * r436133;
        double r436135 = z;
        double r436136 = r436135 * r436135;
        double r436137 = t;
        double r436138 = r436136 - r436137;
        double r436139 = r436134 * r436138;
        double r436140 = r436131 - r436139;
        return r436140;
}

↓

double f(double x, double y, double z, double t) {
        double r436141 = y;
        double r436142 = 4.0;
        double r436143 = r436141 * r436142;
        double r436144 = t;
        double r436145 = z;
        double r436146 = r436145 * r436145;
        double r436147 = r436144 - r436146;
        double r436148 = x;
        double r436149 = r436148 * r436148;
        double r436150 = fma(r436143, r436147, r436149);
        return r436150;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.1
Target	6.0
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 2019199 +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))))