Average Error: 0.0 → 0.1
Time: 4.1s
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 r137723 = x;
        double r137724 = y;
        double r137725 = sin(r137724);
        double r137726 = r137723 + r137725;
        double r137727 = z;
        double r137728 = cos(r137724);
        double r137729 = r137727 * r137728;
        double r137730 = r137726 + r137729;
        return r137730;
}
↓
double f(double x, double y, double z) {
        double r137731 = x;
        double r137732 = y;
        double r137733 = sin(r137732);
        double r137734 = r137731 + r137733;
        double r137735 = z;
        double r137736 = cos(r137732);
        double r137737 = fabs(r137736);
        double r137738 = 0.3333333333333333;
        double r137739 = pow(r137737, r137738);
        double r137740 = r137735 * r137739;
        double r137741 = 2.0;
        double r137742 = pow(r137736, r137741);
        double r137743 = sqrt(r137742);
        double r137744 = pow(r137743, r137738);
        double r137745 = r137740 * r137744;
        double r137746 = cbrt(r137736);
        double r137747 = r137745 * r137746;
        double r137748 = r137734 + r137747;
        return r137748;
}

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*0.2

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

  6. Applied pow1/316.1

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

  7. Applied pow1/316.0

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

  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 2020062 
(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))))