Average Error: 0.1 → 0.4
Time: 25.8s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left(\log \left(e^{{\left(\cos y\right)}^{2}}\right)\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left(\log \left(e^{{\left(\cos y\right)}^{2}}\right)\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r150774 = x;
        double r150775 = y;
        double r150776 = sin(r150775);
        double r150777 = r150774 * r150776;
        double r150778 = z;
        double r150779 = cos(r150775);
        double r150780 = r150778 * r150779;
        double r150781 = r150777 + r150780;
        return r150781;
}
↓
double f(double x, double y, double z) {
        double r150782 = x;
        double r150783 = y;
        double r150784 = sin(r150783);
        double r150785 = r150782 * r150784;
        double r150786 = z;
        double r150787 = cos(r150783);
        double r150788 = 2.0;
        double r150789 = pow(r150787, r150788);
        double r150790 = exp(r150789);
        double r150791 = log(r150790);
        double r150792 = 0.3333333333333333;
        double r150793 = pow(r150791, r150792);
        double r150794 = r150786 * r150793;
        double r150795 = cbrt(r150787);
        double r150796 = r150794 * r150795;
        double r150797 = r150785 + r150796;
        return r150797;
}

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 pow1/316.1

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

  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-log-exp0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019322 
(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))))