Average Error: 0.1 → 0.2
Time: 22.8s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\sqrt[3]{\left(\cos y \cdot \cos y\right) \cdot \left(\left(\cos y \cdot \cos y\right) \cdot \left(\cos y \cdot \cos y\right)\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - \sin y \cdot z\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left(\sqrt[3]{\left(\cos y \cdot \cos y\right) \cdot \left(\left(\cos y \cdot \cos y\right) \cdot \left(\cos y \cdot \cos y\right)\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - \sin y \cdot z
double f(double x, double y, double z) {
        double r8218720 = x;
        double r8218721 = y;
        double r8218722 = cos(r8218721);
        double r8218723 = r8218720 * r8218722;
        double r8218724 = z;
        double r8218725 = sin(r8218721);
        double r8218726 = r8218724 * r8218725;
        double r8218727 = r8218723 - r8218726;
        return r8218727;
}
↓
double f(double x, double y, double z) {
        double r8218728 = x;
        double r8218729 = y;
        double r8218730 = cos(r8218729);
        double r8218731 = r8218730 * r8218730;
        double r8218732 = r8218731 * r8218731;
        double r8218733 = r8218731 * r8218732;
        double r8218734 = cbrt(r8218733);
        double r8218735 = 0.3333333333333333;
        double r8218736 = pow(r8218734, r8218735);
        double r8218737 = r8218728 * r8218736;
        double r8218738 = cbrt(r8218730);
        double r8218739 = r8218737 * r8218738;
        double r8218740 = sin(r8218729);
        double r8218741 = z;
        double r8218742 = r8218740 * r8218741;
        double r8218743 = r8218739 - r8218742;
        return r8218743;
}

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. Using strategy rm

  10. Applied add-cbrt-cube0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))