Average Error: 0.0 → 0.8
Time: 4.5s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\sqrt[3]{x + \cos y} \cdot \sqrt[3]{x + \cos y}, \sqrt[3]{x + \cos y}, -z \cdot \sin y\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\mathsf{fma}\left(\sqrt[3]{x + \cos y} \cdot \sqrt[3]{x + \cos y}, \sqrt[3]{x + \cos y}, -z \cdot \sin y\right)
double f(double x, double y, double z) {
        double r177316 = x;
        double r177317 = y;
        double r177318 = cos(r177317);
        double r177319 = r177316 + r177318;
        double r177320 = z;
        double r177321 = sin(r177317);
        double r177322 = r177320 * r177321;
        double r177323 = r177319 - r177322;
        return r177323;
}
↓
double f(double x, double y, double z) {
        double r177324 = x;
        double r177325 = y;
        double r177326 = cos(r177325);
        double r177327 = r177324 + r177326;
        double r177328 = cbrt(r177327);
        double r177329 = r177328 * r177328;
        double r177330 = z;
        double r177331 = sin(r177325);
        double r177332 = r177330 * r177331;
        double r177333 = -r177332;
        double r177334 = fma(r177329, r177328, r177333);
        return r177334;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(x + \cos y\right) - z \cdot \sin y\]
  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 fma-neg0.8

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

  5. Final simplification0.8

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

Reproduce

herbie shell --seed 2019353 +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))))