Average Error: 0.1 → 0.6
Time: 23.6s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \sqrt[3]{\sin y} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot z\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \sqrt[3]{\sin y} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot z\right)
double f(double x, double y, double z) {
        double r17310050 = x;
        double r17310051 = y;
        double r17310052 = cos(r17310051);
        double r17310053 = r17310050 * r17310052;
        double r17310054 = z;
        double r17310055 = sin(r17310051);
        double r17310056 = r17310054 * r17310055;
        double r17310057 = r17310053 + r17310056;
        return r17310057;
}
↓
double f(double x, double y, double z) {
        double r17310058 = x;
        double r17310059 = y;
        double r17310060 = cos(r17310059);
        double r17310061 = r17310058 * r17310060;
        double r17310062 = sin(r17310059);
        double r17310063 = cbrt(r17310062);
        double r17310064 = r17310063 * r17310063;
        double r17310065 = z;
        double r17310066 = r17310064 * r17310065;
        double r17310067 = r17310063 * r17310066;
        double r17310068 = r17310061 + r17310067;
        return r17310068;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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

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

  4. Applied associate-*r*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))