Average Error: 0.1 → 0.6
Time: 9.8s
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 r201175 = x;
        double r201176 = y;
        double r201177 = sin(r201176);
        double r201178 = r201175 * r201177;
        double r201179 = z;
        double r201180 = cos(r201176);
        double r201181 = r201179 * r201180;
        double r201182 = r201178 + r201181;
        return r201182;
}
↓
double f(double x, double y, double z) {
        double r201183 = x;
        double r201184 = y;
        double r201185 = sin(r201184);
        double r201186 = cbrt(r201185);
        double r201187 = r201186 * r201186;
        double r201188 = r201183 * r201187;
        double r201189 = r201188 * r201186;
        double r201190 = z;
        double r201191 = cos(r201184);
        double r201192 = r201190 * r201191;
        double r201193 = r201189 + r201192;
        return r201193;
}

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 +o rules:numerics
(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))))