Average Error: 0.1 → 0.3
Time: 17.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \sqrt[3]{\left(\cos \left(y + y\right) \cdot \frac{1}{2} + \frac{1}{2}\right) \cdot \cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \sqrt[3]{\left(\cos \left(y + y\right) \cdot \frac{1}{2} + \frac{1}{2}\right) \cdot \cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r10693897 = x;
        double r10693898 = y;
        double r10693899 = cos(r10693898);
        double r10693900 = r10693897 * r10693899;
        double r10693901 = z;
        double r10693902 = sin(r10693898);
        double r10693903 = r10693901 * r10693902;
        double r10693904 = r10693900 - r10693903;
        return r10693904;
}
↓
double f(double x, double y, double z) {
        double r10693905 = x;
        double r10693906 = y;
        double r10693907 = r10693906 + r10693906;
        double r10693908 = cos(r10693907);
        double r10693909 = 0.5;
        double r10693910 = r10693908 * r10693909;
        double r10693911 = r10693910 + r10693909;
        double r10693912 = cos(r10693906);
        double r10693913 = r10693911 * r10693912;
        double r10693914 = cbrt(r10693913);
        double r10693915 = r10693905 * r10693914;
        double r10693916 = z;
        double r10693917 = sin(r10693906);
        double r10693918 = r10693916 * r10693917;
        double r10693919 = r10693915 - r10693918;
        return r10693919;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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 pow1/316.3

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

  7. Applied pow1/316.2

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

  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 sqr-cos0.3

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

  11. Simplified0.3

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

  12. Taylor expanded around inf 16.2

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

  13. Simplified0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))