Average Error: 0.1 → 0.6
Time: 19.7s
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 r7913934 = x;
        double r7913935 = y;
        double r7913936 = cos(r7913935);
        double r7913937 = r7913934 * r7913936;
        double r7913938 = z;
        double r7913939 = sin(r7913935);
        double r7913940 = r7913938 * r7913939;
        double r7913941 = r7913937 + r7913940;
        return r7913941;
}
↓
double f(double x, double y, double z) {
        double r7913942 = x;
        double r7913943 = y;
        double r7913944 = cos(r7913943);
        double r7913945 = r7913942 * r7913944;
        double r7913946 = sin(r7913943);
        double r7913947 = cbrt(r7913946);
        double r7913948 = r7913947 * r7913947;
        double r7913949 = z;
        double r7913950 = r7913948 * r7913949;
        double r7913951 = r7913947 * r7913950;
        double r7913952 = r7913945 + r7913951;
        return r7913952;
}

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

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

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