Average Error: 0.1 → 0.9
Time: 5.8s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \cos y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \cos y\right)
double f(double x, double y, double z) {
        double r219781 = x;
        double r219782 = y;
        double r219783 = sin(r219782);
        double r219784 = r219781 * r219783;
        double r219785 = z;
        double r219786 = cos(r219782);
        double r219787 = r219785 * r219786;
        double r219788 = r219784 + r219787;
        return r219788;
}
↓
double f(double x, double y, double z) {
        double r219789 = x;
        double r219790 = y;
        double r219791 = sin(r219790);
        double r219792 = r219789 * r219791;
        double r219793 = z;
        double r219794 = cbrt(r219793);
        double r219795 = r219794 * r219794;
        double r219796 = cos(r219790);
        double r219797 = r219794 * r219796;
        double r219798 = r219795 * r219797;
        double r219799 = r219792 + r219798;
        return r219799;
}

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-cbrt0.9

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

  4. Applied associate-*l*0.9

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

  5. Final simplification0.9

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

Reproduce

herbie shell --seed 2020060 
(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))))