Average Error: 0.1 → 0.2
Time: 15.5s
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 r151407 = x;
        double r151408 = y;
        double r151409 = sin(r151408);
        double r151410 = r151407 + r151409;
        double r151411 = z;
        double r151412 = cos(r151408);
        double r151413 = r151411 * r151412;
        double r151414 = r151410 + r151413;
        return r151414;
}
↓
double f(double x, double y, double z) {
        double r151415 = x;
        double r151416 = y;
        double r151417 = sin(r151416);
        double r151418 = r151415 + r151417;
        double r151419 = z;
        double r151420 = cos(r151416);
        double r151421 = 2.0;
        double r151422 = pow(r151420, r151421);
        double r151423 = cbrt(r151422);
        double r151424 = r151419 * r151423;
        double r151425 = cbrt(r151420);
        double r151426 = exp(r151425);
        double r151427 = log(r151426);
        double r151428 = r151424 * r151427;
        double r151429 = r151418 + r151428;
        return r151429;
}

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))))