Average Error: 0.1 → 0.2
Time: 5.3s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r187801 = x;
        double r187802 = y;
        double r187803 = sin(r187802);
        double r187804 = r187801 * r187803;
        double r187805 = z;
        double r187806 = cos(r187802);
        double r187807 = r187805 * r187806;
        double r187808 = r187804 + r187807;
        return r187808;
}
↓
double f(double x, double y, double z) {
        double r187809 = x;
        double r187810 = y;
        double r187811 = sin(r187810);
        double r187812 = r187809 * r187811;
        double r187813 = z;
        double r187814 = cos(r187810);
        double r187815 = 2.0;
        double r187816 = pow(r187814, r187815);
        double r187817 = 0.3333333333333333;
        double r187818 = pow(r187816, r187817);
        double r187819 = r187813 * r187818;
        double r187820 = cbrt(r187814);
        double r187821 = r187819 * r187820;
        double r187822 = r187812 + r187821;
        return r187822;
}

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 pow1/315.6

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

  7. Applied pow1/315.5

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 
(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))))