Average Error: 0.1 → 0.7
Time: 4.5s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(z \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}}\right) \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\right) \cdot \sqrt[3]{\sin y}\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(z \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}}\right) \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\right) \cdot \sqrt[3]{\sin y}
double f(double x, double y, double z) {
        double r189175 = x;
        double r189176 = y;
        double r189177 = cos(r189176);
        double r189178 = r189175 * r189177;
        double r189179 = z;
        double r189180 = sin(r189176);
        double r189181 = r189179 * r189180;
        double r189182 = r189178 + r189181;
        return r189182;
}
↓
double f(double x, double y, double z) {
        double r189183 = x;
        double r189184 = y;
        double r189185 = cos(r189184);
        double r189186 = r189183 * r189185;
        double r189187 = z;
        double r189188 = sin(r189184);
        double r189189 = cbrt(r189188);
        double r189190 = r189189 * r189189;
        double r189191 = cbrt(r189190);
        double r189192 = r189189 * r189191;
        double r189193 = cbrt(r189189);
        double r189194 = r189192 * r189193;
        double r189195 = r189187 * r189194;
        double r189196 = r189195 * r189189;
        double r189197 = r189186 + r189196;
        return r189197;
}

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. Using strategy rm

  6. Applied add-cube-cbrt0.6

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

  7. Applied cbrt-prod0.7

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

  8. Applied associate-*r*0.7

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

  9. Final simplification0.7

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

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))