Average Error: 0.1 → 0.5
Time: 26.1s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z} \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{z \cdot \sin y}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\sqrt[3]{z} \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{z \cdot \sin y}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}
double f(double x, double y, double z) {
        double r155723 = x;
        double r155724 = y;
        double r155725 = cos(r155724);
        double r155726 = r155723 * r155725;
        double r155727 = z;
        double r155728 = sin(r155724);
        double r155729 = r155727 * r155728;
        double r155730 = r155726 + r155729;
        return r155730;
}
↓
double f(double x, double y, double z) {
        double r155731 = x;
        double r155732 = y;
        double r155733 = cos(r155732);
        double r155734 = r155731 * r155733;
        double r155735 = z;
        double r155736 = cbrt(r155735);
        double r155737 = sin(r155732);
        double r155738 = cbrt(r155737);
        double r155739 = r155735 * r155737;
        double r155740 = cbrt(r155739);
        double r155741 = r155738 * r155740;
        double r155742 = r155736 * r155741;
        double r155743 = r155742 * r155740;
        double r155744 = r155734 + r155743;
        return r155744;
}

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

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

  5. Applied cbrt-prod0.5

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

  6. Applied associate-*l*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2019303 +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))))