Average Error: 0.1 → 0.2
Time: 17.2s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left(\sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{3}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left(\sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{3}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r254784 = x;
        double r254785 = y;
        double r254786 = sin(r254785);
        double r254787 = r254784 * r254786;
        double r254788 = z;
        double r254789 = cos(r254785);
        double r254790 = r254788 * r254789;
        double r254791 = r254787 + r254790;
        return r254791;
}
↓
double f(double x, double y, double z) {
        double r254792 = x;
        double r254793 = y;
        double r254794 = sin(r254793);
        double r254795 = r254792 * r254794;
        double r254796 = z;
        double r254797 = cos(r254793);
        double r254798 = 2.0;
        double r254799 = pow(r254797, r254798);
        double r254800 = 3.0;
        double r254801 = pow(r254799, r254800);
        double r254802 = cbrt(r254801);
        double r254803 = 0.3333333333333333;
        double r254804 = pow(r254802, r254803);
        double r254805 = r254796 * r254804;
        double r254806 = cbrt(r254797);
        double r254807 = r254805 * r254806;
        double r254808 = r254795 + r254807;
        return r254808;
}

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 pow1/316.2

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

  7. Applied pow1/316.2

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

  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 add-cbrt-cube0.2

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

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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))))