Average Error: 0.1 → 0.2
Time: 22.8s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{6}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{6}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r163049 = x;
        double r163050 = y;
        double r163051 = cos(r163050);
        double r163052 = r163049 * r163051;
        double r163053 = z;
        double r163054 = sin(r163050);
        double r163055 = r163053 * r163054;
        double r163056 = r163052 - r163055;
        return r163056;
}
↓
double f(double x, double y, double z) {
        double r163057 = x;
        double r163058 = y;
        double r163059 = cos(r163058);
        double r163060 = 6.0;
        double r163061 = pow(r163059, r163060);
        double r163062 = cbrt(r163061);
        double r163063 = 0.3333333333333333;
        double r163064 = pow(r163062, r163063);
        double r163065 = r163057 * r163064;
        double r163066 = cbrt(r163059);
        double r163067 = r163065 * r163066;
        double r163068 = z;
        double r163069 = sin(r163058);
        double r163070 = r163068 * r163069;
        double r163071 = r163067 - r163070;
        return r163071;
}

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. 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-cbrt-cube0.2

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

  12. Simplified0.2

    \[\leadsto \left(x \cdot {\left(\sqrt[3]{\color{blue}{{\left(\cos y\right)}^{6}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  13. Final simplification0.2

    \[\leadsto \left(x \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{6}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

Reproduce

herbie shell --seed 2019323 +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))))