Average Error: 0.1 → 0.5
Time: 15.3s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(\left(\sqrt[3]{x \cdot \sin y} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{x \cdot \sin y} + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(\left(\sqrt[3]{x \cdot \sin y} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{x \cdot \sin y} + z \cdot \cos y
double f(double x, double y, double z) {
        double r197757 = x;
        double r197758 = y;
        double r197759 = sin(r197758);
        double r197760 = r197757 * r197759;
        double r197761 = z;
        double r197762 = cos(r197758);
        double r197763 = r197761 * r197762;
        double r197764 = r197760 + r197763;
        return r197764;
}
↓
double f(double x, double y, double z) {
        double r197765 = x;
        double r197766 = y;
        double r197767 = sin(r197766);
        double r197768 = r197765 * r197767;
        double r197769 = cbrt(r197768);
        double r197770 = cbrt(r197765);
        double r197771 = r197769 * r197770;
        double r197772 = cbrt(r197767);
        double r197773 = r197771 * r197772;
        double r197774 = r197773 * r197769;
        double r197775 = z;
        double r197776 = cos(r197766);
        double r197777 = r197775 * r197776;
        double r197778 = r197774 + r197777;
        return r197778;
}

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

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

  5. Applied cbrt-prod0.5

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

  6. Applied associate-*r*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2019298 
(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))))