Average Error: 0.1 → 0.2
Time: 16.7s
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 r137668 = x;
        double r137669 = y;
        double r137670 = sin(r137669);
        double r137671 = r137668 + r137670;
        double r137672 = z;
        double r137673 = cos(r137669);
        double r137674 = r137672 * r137673;
        double r137675 = r137671 + r137674;
        return r137675;
}
↓
double f(double x, double y, double z) {
        double r137676 = x;
        double r137677 = y;
        double r137678 = sin(r137677);
        double r137679 = r137676 + r137678;
        double r137680 = z;
        double r137681 = cos(r137677);
        double r137682 = 2.0;
        double r137683 = pow(r137681, r137682);
        double r137684 = cbrt(r137683);
        double r137685 = r137680 * r137684;
        double r137686 = cbrt(r137681);
        double r137687 = exp(r137686);
        double r137688 = log(r137687);
        double r137689 = r137685 * r137688;
        double r137690 = r137679 + r137689;
        return r137690;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 +o rules:numerics
(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))))