Average Error: 0.1 → 0.6
Time: 21.1s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r9818756 = x;
        double r9818757 = y;
        double r9818758 = cos(r9818757);
        double r9818759 = r9818756 * r9818758;
        double r9818760 = z;
        double r9818761 = sin(r9818757);
        double r9818762 = r9818760 * r9818761;
        double r9818763 = r9818759 + r9818762;
        return r9818763;
}
↓
double f(double x, double y, double z) {
        double r9818764 = x;
        double r9818765 = y;
        double r9818766 = cos(r9818765);
        double r9818767 = r9818764 * r9818766;
        double r9818768 = z;
        double r9818769 = cbrt(r9818768);
        double r9818770 = r9818769 * r9818769;
        double r9818771 = sin(r9818765);
        double r9818772 = r9818771 * r9818769;
        double r9818773 = r9818770 * r9818772;
        double r9818774 = r9818767 + r9818773;
        return r9818774;
}

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

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

  4. Applied associate-*l*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))