Average Error: 0.1 → 0.6
Time: 5.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y} + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y} + z \cdot \cos y
double f(double x, double y, double z) {
        double r217750 = x;
        double r217751 = y;
        double r217752 = sin(r217751);
        double r217753 = r217750 * r217752;
        double r217754 = z;
        double r217755 = cos(r217751);
        double r217756 = r217754 * r217755;
        double r217757 = r217753 + r217756;
        return r217757;
}
↓
double f(double x, double y, double z) {
        double r217758 = x;
        double r217759 = y;
        double r217760 = sin(r217759);
        double r217761 = cbrt(r217760);
        double r217762 = r217761 * r217761;
        double r217763 = r217758 * r217762;
        double r217764 = r217763 * r217761;
        double r217765 = z;
        double r217766 = cos(r217759);
        double r217767 = r217765 * r217766;
        double r217768 = r217764 + r217767;
        return r217768;
}

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-cbrt0.6

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

  4. Applied associate-*r*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2020003 
(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))))