Average Error: 0.1 → 0.6
Time: 25.6s
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 r121179 = x;
        double r121180 = y;
        double r121181 = sin(r121180);
        double r121182 = r121179 * r121181;
        double r121183 = z;
        double r121184 = cos(r121180);
        double r121185 = r121183 * r121184;
        double r121186 = r121182 + r121185;
        return r121186;
}
↓
double f(double x, double y, double z) {
        double r121187 = x;
        double r121188 = y;
        double r121189 = sin(r121188);
        double r121190 = cbrt(r121189);
        double r121191 = r121190 * r121190;
        double r121192 = r121187 * r121191;
        double r121193 = r121192 * r121190;
        double r121194 = z;
        double r121195 = cos(r121188);
        double r121196 = r121194 * r121195;
        double r121197 = r121193 + r121196;
        return r121197;
}

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 2019304 
(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))))