Average Error: 0.1 → 0.2
Time: 17.7s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\left(x + \sin y\right) + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right)\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\left(x + \sin y\right) + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right)
double f(double x, double y, double z) {
        double r787294 = x;
        double r787295 = y;
        double r787296 = sin(r787295);
        double r787297 = r787294 + r787296;
        double r787298 = z;
        double r787299 = cos(r787295);
        double r787300 = r787298 * r787299;
        double r787301 = r787297 + r787300;
        return r787301;
}
↓
double f(double x, double y, double z) {
        double r787302 = x;
        double r787303 = y;
        double r787304 = sin(r787303);
        double r787305 = r787302 + r787304;
        double r787306 = z;
        double r787307 = cos(r787303);
        double r787308 = 2.0;
        double r787309 = pow(r787307, r787308);
        double r787310 = cbrt(r787309);
        double r787311 = r787306 * r787310;
        double r787312 = cbrt(r787307);
        double r787313 = exp(r787312);
        double r787314 = log(r787313);
        double r787315 = r787311 * r787314;
        double r787316 = r787305 + r787315;
        return r787316;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt0.2

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

  4. Applied associate-*r*0.2

    \[\leadsto \left(x + \sin y\right) + \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}}\]
  5. Using strategy rm

  6. Applied cbrt-unprod0.2

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

  7. Simplified0.2

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \sqrt[3]{\color{blue}{{\left(\cos y\right)}^{2}}}\right) \cdot \sqrt[3]{\cos y}\]
  8. Using strategy rm

  9. Applied add-log-exp0.2

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \color{blue}{\log \left(e^{\sqrt[3]{\cos y}}\right)}\]

  10. Final simplification0.2

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right)\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))