Average Error: 0.1 → 0.3
Time: 24.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(\sqrt[3]{\sqrt[3]{\left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right) \cdot \left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right)}} \cdot \left(\sqrt[3]{\sqrt[3]{\left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right) \cdot \left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right) \cdot \left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right)}}\right)\right)}^{\frac{1}{3}} \cdot x\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left({\left(\sqrt[3]{\sqrt[3]{\left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right) \cdot \left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right)}} \cdot \left(\sqrt[3]{\sqrt[3]{\left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right) \cdot \left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right)}} \cdot \sqrt[3]{\sqrt[3]{\left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right) \cdot \left(\cos y \cdot \left(\cos y \cdot \cos y\right)\right)}}\right)\right)}^{\frac{1}{3}} \cdot x\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r10983955 = x;
        double r10983956 = y;
        double r10983957 = cos(r10983956);
        double r10983958 = r10983955 * r10983957;
        double r10983959 = z;
        double r10983960 = sin(r10983956);
        double r10983961 = r10983959 * r10983960;
        double r10983962 = r10983958 - r10983961;
        return r10983962;
}
↓
double f(double x, double y, double z) {
        double r10983963 = y;
        double r10983964 = cos(r10983963);
        double r10983965 = cbrt(r10983964);
        double r10983966 = r10983964 * r10983964;
        double r10983967 = r10983964 * r10983966;
        double r10983968 = r10983967 * r10983967;
        double r10983969 = cbrt(r10983968);
        double r10983970 = cbrt(r10983969);
        double r10983971 = r10983970 * r10983970;
        double r10983972 = r10983970 * r10983971;
        double r10983973 = 0.3333333333333333;
        double r10983974 = pow(r10983972, r10983973);
        double r10983975 = x;
        double r10983976 = r10983974 * r10983975;
        double r10983977 = r10983965 * r10983976;
        double r10983978 = z;
        double r10983979 = sin(r10983963);
        double r10983980 = r10983978 * r10983979;
        double r10983981 = r10983977 - r10983980;
        return r10983981;
}

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 pow1/316.0

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

  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. Using strategy rm

  10. Applied add-cbrt-cube0.2

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

  11. Applied add-cbrt-cube0.3

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

  12. Applied cbrt-unprod0.2

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

  14. Applied add-cube-cbrt0.3

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

  15. Final simplification0.3

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))