Average Error: 0.0 → 0.8
Time: 4.4s
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 r153277 = x;
        double r153278 = y;
        double r153279 = cos(r153278);
        double r153280 = r153277 + r153279;
        double r153281 = z;
        double r153282 = sin(r153278);
        double r153283 = r153281 * r153282;
        double r153284 = r153280 - r153283;
        return r153284;
}
↓
double f(double x, double y, double z) {
        double r153285 = x;
        double r153286 = y;
        double r153287 = cos(r153286);
        double r153288 = r153285 + r153287;
        double r153289 = cbrt(r153288);
        double r153290 = r153289 * r153289;
        double r153291 = z;
        double r153292 = sin(r153286);
        double r153293 = r153291 * r153292;
        double r153294 = -r153293;
        double r153295 = fma(r153290, r153289, r153294);
        return r153295;
}

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))))