Average Error: 0.1 → 0.3
Time: 13.7s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(\left(x \cdot \sqrt{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left(\left(x \cdot \sqrt{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r4364850 = x;
        double r4364851 = y;
        double r4364852 = cos(r4364851);
        double r4364853 = r4364850 * r4364852;
        double r4364854 = z;
        double r4364855 = sin(r4364851);
        double r4364856 = r4364854 * r4364855;
        double r4364857 = r4364853 - r4364856;
        return r4364857;
}
↓
double f(double x, double y, double z) {
        double r4364858 = y;
        double r4364859 = cos(r4364858);
        double r4364860 = cbrt(r4364859);
        double r4364861 = x;
        double r4364862 = r4364859 * r4364859;
        double r4364863 = 0.3333333333333333;
        double r4364864 = pow(r4364862, r4364863);
        double r4364865 = sqrt(r4364864);
        double r4364866 = r4364861 * r4364865;
        double r4364867 = r4364866 * r4364865;
        double r4364868 = r4364860 * r4364867;
        double r4364869 = z;
        double r4364870 = sin(r4364858);
        double r4364871 = r4364869 * r4364870;
        double r4364872 = r4364868 - r4364871;
        return r4364872;
}

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 pow1/316.0

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

  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-sqr-sqrt0.3

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

  11. Applied associate-*r*0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))