Average Error: 0.1 → 0.2
Time: 24.1s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + z \cdot \sqrt[3]{{\left(\cos y\right)}^{3}}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + z \cdot \sqrt[3]{{\left(\cos y\right)}^{3}}
double f(double x, double y, double z) {
        double r135753 = x;
        double r135754 = y;
        double r135755 = sin(r135754);
        double r135756 = r135753 * r135755;
        double r135757 = z;
        double r135758 = cos(r135754);
        double r135759 = r135757 * r135758;
        double r135760 = r135756 + r135759;
        return r135760;
}
↓
double f(double x, double y, double z) {
        double r135761 = x;
        double r135762 = y;
        double r135763 = sin(r135762);
        double r135764 = r135761 * r135763;
        double r135765 = z;
        double r135766 = cos(r135762);
        double r135767 = 3.0;
        double r135768 = pow(r135766, r135767);
        double r135769 = cbrt(r135768);
        double r135770 = r135765 * r135769;
        double r135771 = r135764 + r135770;
        return r135771;
}

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 cbrt-unprod0.3

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

  7. Simplified0.3

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

  9. Applied associate-*l*0.3

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

  11. Applied cbrt-unprod0.2

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

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019325 
(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))))