Average Error: 0.1 → 0.3
Time: 5.0s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r183743 = x;
        double r183744 = y;
        double r183745 = sin(r183744);
        double r183746 = r183743 * r183745;
        double r183747 = z;
        double r183748 = cos(r183744);
        double r183749 = r183747 * r183748;
        double r183750 = r183746 + r183749;
        return r183750;
}
↓
double f(double x, double y, double z) {
        double r183751 = x;
        double r183752 = y;
        double r183753 = sin(r183752);
        double r183754 = r183751 * r183753;
        double r183755 = z;
        double r183756 = cos(r183752);
        double r183757 = 2.0;
        double r183758 = pow(r183756, r183757);
        double r183759 = cbrt(r183758);
        double r183760 = r183755 * r183759;
        double r183761 = cbrt(r183756);
        double r183762 = r183760 * r183761;
        double r183763 = r183754 + r183762;
        return r183763;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied cbrt-unprod0.3

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

  7. Simplified0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{\color{blue}{{\left(\cos y\right)}^{2}}}\right) \cdot \sqrt[3]{\cos y}\]

  8. Final simplification0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(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))))