Average Error: 0.1 → 0.4
Time: 16.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(\left(\log \left(e^{\sqrt[3]{\cos y}}\right) \cdot x\right) \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(\left(\log \left(e^{\sqrt[3]{\cos y}}\right) \cdot x\right) \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r148762 = x;
        double r148763 = y;
        double r148764 = cos(r148763);
        double r148765 = r148762 * r148764;
        double r148766 = z;
        double r148767 = sin(r148763);
        double r148768 = r148766 * r148767;
        double r148769 = r148765 - r148768;
        return r148769;
}
↓
double f(double x, double y, double z) {
        double r148770 = y;
        double r148771 = cos(r148770);
        double r148772 = cbrt(r148771);
        double r148773 = exp(r148772);
        double r148774 = log(r148773);
        double r148775 = x;
        double r148776 = r148774 * r148775;
        double r148777 = r148776 * r148772;
        double r148778 = r148777 * r148772;
        double r148779 = z;
        double r148780 = sin(r148770);
        double r148781 = r148779 * r148780;
        double r148782 = r148778 - r148781;
        return r148782;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  5. Simplified0.4

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

  7. Applied add-log-exp0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))