Average Error: 0.1 → 0.2
Time: 9.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + z \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\cos y}\right)\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + z \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\cos y}\right)
double f(double x, double y, double z) {
        double r139679 = x;
        double r139680 = y;
        double r139681 = sin(r139680);
        double r139682 = r139679 * r139681;
        double r139683 = z;
        double r139684 = cos(r139680);
        double r139685 = r139683 * r139684;
        double r139686 = r139682 + r139685;
        return r139686;
}
↓
double f(double x, double y, double z) {
        double r139687 = x;
        double r139688 = y;
        double r139689 = sin(r139688);
        double r139690 = r139687 * r139689;
        double r139691 = z;
        double r139692 = cos(r139688);
        double r139693 = 2.0;
        double r139694 = pow(r139692, r139693);
        double r139695 = 0.3333333333333333;
        double r139696 = pow(r139694, r139695);
        double r139697 = cbrt(r139692);
        double r139698 = r139696 * r139697;
        double r139699 = r139691 * r139698;
        double r139700 = r139690 + r139699;
        return r139700;
}

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 pow1/316.9

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

  7. Applied pow1/316.9

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

  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 associate-*l*0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2019308 
(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))))