Average Error: 0.1 → 0.6
Time: 5.6s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\sin y}\right)\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\sin y}\right)\right)
double f(double x, double y, double z) {
        double r209644 = x;
        double r209645 = y;
        double r209646 = cos(r209645);
        double r209647 = r209644 * r209646;
        double r209648 = z;
        double r209649 = sin(r209645);
        double r209650 = r209648 * r209649;
        double r209651 = r209647 + r209650;
        return r209651;
}
↓
double f(double x, double y, double z) {
        double r209652 = x;
        double r209653 = y;
        double r209654 = cos(r209653);
        double r209655 = r209652 * r209654;
        double r209656 = z;
        double r209657 = sin(r209653);
        double r209658 = cbrt(r209657);
        double r209659 = r209658 * r209658;
        double r209660 = r209656 * r209659;
        double r209661 = expm1(r209658);
        double r209662 = log1p(r209661);
        double r209663 = r209660 * r209662;
        double r209664 = r209655 + r209663;
        return r209664;
}

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-cbrt0.6

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

  4. Applied associate-*r*0.6

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

  6. Applied log1p-expm1-u0.6

    \[\leadsto x \cdot \cos y + \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\sin y}\right)\right)}\]

  7. Final simplification0.6

    \[\leadsto x \cdot \cos y + \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{\sin y}\right)\right)\]

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))