Average Error: 0.1 → 0.2
Time: 5.2s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\cos y}\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\cos y}\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r201972 = x;
        double r201973 = y;
        double r201974 = cos(r201973);
        double r201975 = r201972 * r201974;
        double r201976 = z;
        double r201977 = sin(r201973);
        double r201978 = r201976 * r201977;
        double r201979 = r201975 - r201978;
        return r201979;
}
↓
double f(double x, double y, double z) {
        double r201980 = x;
        double r201981 = y;
        double r201982 = cos(r201981);
        double r201983 = 2.0;
        double r201984 = pow(r201982, r201983);
        double r201985 = 0.3333333333333333;
        double r201986 = pow(r201984, r201985);
        double r201987 = cbrt(r201982);
        double r201988 = r201986 * r201987;
        double r201989 = r201980 * r201988;
        double r201990 = z;
        double r201991 = sin(r201981);
        double r201992 = r201990 * r201991;
        double r201993 = r201989 - r201992;
        return r201993;
}

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 pow1/316.4

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

  7. Applied pow1/316.3

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

  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 associate-*l*0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))