Average Error: 0.1 → 0.6
Time: 15.2s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y} + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y} + z \cdot \cos y
double f(double x, double y, double z) {
        double r240744 = x;
        double r240745 = y;
        double r240746 = sin(r240745);
        double r240747 = r240744 * r240746;
        double r240748 = z;
        double r240749 = cos(r240745);
        double r240750 = r240748 * r240749;
        double r240751 = r240747 + r240750;
        return r240751;
}
↓
double f(double x, double y, double z) {
        double r240752 = x;
        double r240753 = y;
        double r240754 = sin(r240753);
        double r240755 = cbrt(r240754);
        double r240756 = r240755 * r240755;
        double r240757 = r240752 * r240756;
        double r240758 = r240757 * r240755;
        double r240759 = z;
        double r240760 = cos(r240753);
        double r240761 = r240759 * r240760;
        double r240762 = r240758 + r240761;
        return r240762;
}

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-cbrt0.6

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

  4. Applied associate-*r*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2020047 
(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))))