Average Error: 0.1 → 0.0
Time: 17.1s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\mathsf{fma}\left(z, -\sin y, \cos y + x\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\mathsf{fma}\left(z, -\sin y, \cos y + x\right)
double f(double x, double y, double z) {
        double r114527 = x;
        double r114528 = y;
        double r114529 = cos(r114528);
        double r114530 = r114527 + r114529;
        double r114531 = z;
        double r114532 = sin(r114528);
        double r114533 = r114531 * r114532;
        double r114534 = r114530 - r114533;
        return r114534;
}
↓
double f(double x, double y, double z) {
        double r114535 = z;
        double r114536 = y;
        double r114537 = sin(r114536);
        double r114538 = -r114537;
        double r114539 = cos(r114536);
        double r114540 = x;
        double r114541 = r114539 + r114540;
        double r114542 = fma(r114535, r114538, r114541);
        return r114542;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[\left(x + \cos y\right) - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{x + \cos y} \cdot \sqrt[3]{x + \cos y}\right) \cdot \sqrt[3]{x + \cos y}} - z \cdot \sin y\]

  4. Applied prod-diff0.8

    \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x + \cos y} \cdot \sqrt[3]{x + \cos y}, \sqrt[3]{x + \cos y}, -\sin y \cdot z\right) + \mathsf{fma}\left(-\sin y, z, \sin y \cdot z\right)}\]

  5. Simplified0.1

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

  6. Simplified0.0

    \[\leadsto \mathsf{fma}\left(z, -\sin y, \cos y + x\right) + \color{blue}{0}\]

  7. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z, -\sin y, \cos y + x\right)\]

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))