Average Error: 0.1 → 0.6
Time: 22.8s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \sqrt[3]{\sin y \cdot z} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \sqrt[3]{\sin y \cdot z} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r9424757 = x;
        double r9424758 = y;
        double r9424759 = cos(r9424758);
        double r9424760 = r9424757 * r9424759;
        double r9424761 = z;
        double r9424762 = sin(r9424758);
        double r9424763 = r9424761 * r9424762;
        double r9424764 = r9424760 - r9424763;
        return r9424764;
}
↓
double f(double x, double y, double z) {
        double r9424765 = x;
        double r9424766 = y;
        double r9424767 = cos(r9424766);
        double r9424768 = r9424765 * r9424767;
        double r9424769 = sin(r9424766);
        double r9424770 = z;
        double r9424771 = r9424769 * r9424770;
        double r9424772 = cbrt(r9424771);
        double r9424773 = cbrt(r9424769);
        double r9424774 = r9424773 * r9424773;
        double r9424775 = cbrt(r9424770);
        double r9424776 = r9424775 * r9424775;
        double r9424777 = r9424774 * r9424776;
        double r9424778 = r9424772 * r9424777;
        double r9424779 = r9424768 - r9424778;
        return r9424779;
}

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

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

  6. Applied cbrt-prod0.6

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

  7. Applied swap-sqr0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))