Average Error: 0.0 → 0.1
Time: 4.8s
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 r172855 = x;
        double r172856 = y;
        double r172857 = sin(r172856);
        double r172858 = r172855 + r172857;
        double r172859 = z;
        double r172860 = cos(r172856);
        double r172861 = r172859 * r172860;
        double r172862 = r172858 + r172861;
        return r172862;
}
↓
double f(double x, double y, double z) {
        double r172863 = x;
        double r172864 = y;
        double r172865 = sin(r172864);
        double r172866 = r172863 + r172865;
        double r172867 = z;
        double r172868 = cos(r172864);
        double r172869 = fabs(r172868);
        double r172870 = 0.3333333333333333;
        double r172871 = pow(r172869, r172870);
        double r172872 = r172867 * r172871;
        double r172873 = 2.0;
        double r172874 = pow(r172868, r172873);
        double r172875 = sqrt(r172874);
        double r172876 = pow(r172875, r172870);
        double r172877 = r172872 * r172876;
        double r172878 = cbrt(r172868);
        double r172879 = r172877 * r172878;
        double r172880 = r172866 + r172879;
        return r172880;
}

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))))