Average Error: 0.1 → 0.6
Time: 26.7s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r114798 = x;
        double r114799 = y;
        double r114800 = cos(r114799);
        double r114801 = r114798 * r114800;
        double r114802 = z;
        double r114803 = sin(r114799);
        double r114804 = r114802 * r114803;
        double r114805 = r114801 + r114804;
        return r114805;
}
↓
double f(double x, double y, double z) {
        double r114806 = x;
        double r114807 = y;
        double r114808 = cos(r114807);
        double r114809 = r114806 * r114808;
        double r114810 = z;
        double r114811 = cbrt(r114810);
        double r114812 = r114811 * r114811;
        double r114813 = sin(r114807);
        double r114814 = r114811 * r114813;
        double r114815 = r114812 * r114814;
        double r114816 = r114809 + r114815;
        return r114816;
}

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

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))