Average Error: 0.1 → 0.3
Time: 26.2s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot z\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot z\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r189790 = x;
        double r189791 = y;
        double r189792 = sin(r189791);
        double r189793 = r189790 * r189792;
        double r189794 = z;
        double r189795 = cos(r189791);
        double r189796 = r189794 * r189795;
        double r189797 = r189793 + r189796;
        return r189797;
}
↓
double f(double x, double y, double z) {
        double r189798 = x;
        double r189799 = y;
        double r189800 = sin(r189799);
        double r189801 = r189798 * r189800;
        double r189802 = cos(r189799);
        double r189803 = 2.0;
        double r189804 = pow(r189802, r189803);
        double r189805 = cbrt(r189804);
        double r189806 = z;
        double r189807 = r189805 * r189806;
        double r189808 = cbrt(r189802);
        double r189809 = r189807 * r189808;
        double r189810 = r189801 + r189809;
        return r189810;
}

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 0.1

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.0

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

  7. Applied pow1/316.0

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

  8. Applied pow-prod-down0.2

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

  9. Simplified0.2

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

  11. Applied *-un-lft-identity0.2

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

  12. Applied cbrt-prod0.2

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

  13. Applied associate-*r*0.2

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

  14. Simplified0.3

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

  15. Final simplification0.3

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))