Average Error: 0.0 → 0.1
Time: 7.8s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\left(x + \sin y\right) + \left(\left(z \cdot {\left(\left|\cos y\right|\right)}^{\frac{1}{3}}\right) \cdot {\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\left(x + \sin y\right) + \left(\left(z \cdot {\left(\left|\cos y\right|\right)}^{\frac{1}{3}}\right) \cdot {\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r804 = x;
        double r805 = y;
        double r806 = sin(r805);
        double r807 = r804 + r806;
        double r808 = z;
        double r809 = cos(r805);
        double r810 = r808 * r809;
        double r811 = r807 + r810;
        return r811;
}
↓
double f(double x, double y, double z) {
        double r812 = x;
        double r813 = y;
        double r814 = sin(r813);
        double r815 = r812 + r814;
        double r816 = z;
        double r817 = cos(r813);
        double r818 = fabs(r817);
        double r819 = 0.3333333333333333;
        double r820 = pow(r818, r819);
        double r821 = r816 * r820;
        double r822 = 2.0;
        double r823 = pow(r817, r822);
        double r824 = sqrt(r823);
        double r825 = pow(r824, r819);
        double r826 = r821 * r825;
        double r827 = cbrt(r817);
        double r828 = r826 * r827;
        double r829 = r815 + r828;
        return r829;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x + \sin y\right) + z \cdot \cos y\]
  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*0.3

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

  6. Applied pow1/316.3

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y}\]

  7. Applied pow1/316.3

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \left(\color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}} \cdot {\left(\cos y\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y}\]

  8. Applied pow-prod-down0.1

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \color{blue}{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}\]

  9. Simplified0.1

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot {\color{blue}{\left({\left(\cos y\right)}^{2}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
  10. Using strategy rm

  11. Applied add-sqr-sqrt0.1

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot {\color{blue}{\left(\sqrt{{\left(\cos y\right)}^{2}} \cdot \sqrt{{\left(\cos y\right)}^{2}}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]

  12. Applied unpow-prod-down0.1

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \color{blue}{\left({\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}} \cdot {\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right)}\right) \cdot \sqrt[3]{\cos y}\]

  13. Applied associate-*r*0.1

    \[\leadsto \left(x + \sin y\right) + \color{blue}{\left(\left(z \cdot {\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot {\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right)} \cdot \sqrt[3]{\cos y}\]

  14. Simplified0.1

    \[\leadsto \left(x + \sin y\right) + \left(\color{blue}{\left(z \cdot {\left(\left|\cos y\right|\right)}^{\frac{1}{3}}\right)} \cdot {\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]

  15. Final simplification0.1

    \[\leadsto \left(x + \sin y\right) + \left(\left(z \cdot {\left(\left|\cos y\right|\right)}^{\frac{1}{3}}\right) \cdot {\left(\sqrt{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2020025 +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))))