Average Error: 0.1 → 0.2
Time: 4.8s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left(e^{\log \left({\left(\cos y\right)}^{2}\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\left(e^{\log \left({\left(\cos y\right)}^{2}\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r154700 = x;
        double r154701 = y;
        double r154702 = cos(r154701);
        double r154703 = r154700 * r154702;
        double r154704 = z;
        double r154705 = sin(r154701);
        double r154706 = r154704 * r154705;
        double r154707 = r154703 + r154706;
        return r154707;
}
↓
double f(double x, double y, double z) {
        double r154708 = x;
        double r154709 = y;
        double r154710 = cos(r154709);
        double r154711 = 2.0;
        double r154712 = pow(r154710, r154711);
        double r154713 = log(r154712);
        double r154714 = exp(r154713);
        double r154715 = 0.3333333333333333;
        double r154716 = pow(r154714, r154715);
        double r154717 = r154708 * r154716;
        double r154718 = cbrt(r154710);
        double r154719 = r154717 * r154718;
        double r154720 = z;
        double r154721 = sin(r154709);
        double r154722 = r154720 * r154721;
        double r154723 = r154719 + r154722;
        return r154723;
}

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

    \[x \cdot \cos y + z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.1

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

  7. Applied pow1/316.1

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

  8. Applied pow-prod-down0.2

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

  9. Simplified0.2

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

  11. Applied add-exp-log16.1

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

  12. Applied pow-exp16.1

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))