Average Error: 0.1 → 0.4
Time: 15.7s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r179783 = x;
        double r179784 = y;
        double r179785 = sin(r179784);
        double r179786 = r179783 * r179785;
        double r179787 = z;
        double r179788 = cos(r179784);
        double r179789 = r179787 * r179788;
        double r179790 = r179786 + r179789;
        return r179790;
}
↓
double f(double x, double y, double z) {
        double r179791 = x;
        double r179792 = y;
        double r179793 = sin(r179792);
        double r179794 = r179791 * r179793;
        double r179795 = z;
        double r179796 = cos(r179792);
        double r179797 = cbrt(r179796);
        double r179798 = r179797 * r179797;
        double r179799 = r179795 * r179798;
        double r179800 = r179799 * r179797;
        double r179801 = r179794 + r179800;
        return r179801;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))