Average Error: 0.1 → 0.6
Time: 9.4s
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 r267045 = x;
        double r267046 = y;
        double r267047 = sin(r267046);
        double r267048 = r267045 * r267047;
        double r267049 = z;
        double r267050 = cos(r267046);
        double r267051 = r267049 * r267050;
        double r267052 = r267048 + r267051;
        return r267052;
}
↓
double f(double x, double y, double z) {
        double r267053 = x;
        double r267054 = y;
        double r267055 = sin(r267054);
        double r267056 = cbrt(r267055);
        double r267057 = r267056 * r267056;
        double r267058 = r267053 * r267057;
        double r267059 = r267058 * r267056;
        double r267060 = z;
        double r267061 = cos(r267054);
        double r267062 = r267060 * r267061;
        double r267063 = r267059 + r267062;
        return r267063;
}

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 2020047 
(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))))