Average Error: 0.1 → 0.7
Time: 15.5s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)
double f(double x, double y, double z) {
        double r120715 = x;
        double r120716 = y;
        double r120717 = cos(r120716);
        double r120718 = r120715 * r120717;
        double r120719 = z;
        double r120720 = sin(r120716);
        double r120721 = r120719 * r120720;
        double r120722 = r120718 + r120721;
        return r120722;
}
↓
double f(double x, double y, double z) {
        double r120723 = x;
        double r120724 = y;
        double r120725 = cos(r120724);
        double r120726 = r120723 * r120725;
        double r120727 = z;
        double r120728 = sin(r120724);
        double r120729 = cbrt(r120728);
        double r120730 = r120729 * r120729;
        double r120731 = r120727 * r120730;
        double r120732 = cbrt(r120730);
        double r120733 = cbrt(r120729);
        double r120734 = r120732 * r120733;
        double r120735 = r120731 * r120734;
        double r120736 = r120726 + r120735;
        return r120736;
}

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

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

  7. Applied cbrt-prod0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))