Average Error: 0.1 → 0.3
Time: 19.5s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}}}\right) \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}}}\right) \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r825823 = x;
        double r825824 = y;
        double r825825 = cos(r825824);
        double r825826 = r825823 * r825825;
        double r825827 = z;
        double r825828 = sin(r825824);
        double r825829 = r825827 * r825828;
        double r825830 = r825826 + r825829;
        return r825830;
}
↓
double f(double x, double y, double z) {
        double r825831 = x;
        double r825832 = y;
        double r825833 = cos(r825832);
        double r825834 = 2.0;
        double r825835 = pow(r825833, r825834);
        double r825836 = 0.6666666666666666;
        double r825837 = pow(r825835, r825836);
        double r825838 = cbrt(r825837);
        double r825839 = r825831 * r825838;
        double r825840 = cbrt(r825835);
        double r825841 = 0.3333333333333333;
        double r825842 = pow(r825840, r825841);
        double r825843 = r825839 * r825842;
        double r825844 = cbrt(r825833);
        double r825845 = r825843 * r825844;
        double r825846 = z;
        double r825847 = sin(r825832);
        double r825848 = r825846 * r825847;
        double r825849 = r825845 + r825848;
        return r825849;
}

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 pow1/315.6

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

  7. Applied pow1/315.6

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

  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-cube-cbrt0.3

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

  12. Applied unpow-prod-down0.3

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

  13. Applied associate-*r*0.3

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

  14. Simplified0.3

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

  15. Final simplification0.3

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))