Average Error: 0.1 → 0.5
Time: 5.0s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right)\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right)\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r196616 = x;
        double r196617 = y;
        double r196618 = sin(r196617);
        double r196619 = r196616 * r196618;
        double r196620 = z;
        double r196621 = cos(r196617);
        double r196622 = r196620 * r196621;
        double r196623 = r196619 + r196622;
        return r196623;
}
↓
double f(double x, double y, double z) {
        double r196624 = x;
        double r196625 = y;
        double r196626 = sin(r196625);
        double r196627 = r196624 * r196626;
        double r196628 = z;
        double r196629 = cos(r196625);
        double r196630 = cbrt(r196629);
        double r196631 = cbrt(r196630);
        double r196632 = r196631 * r196631;
        double r196633 = r196632 * r196631;
        double r196634 = r196630 * r196633;
        double r196635 = r196628 * r196634;
        double r196636 = r196635 * r196630;
        double r196637 = r196627 + r196636;
        return r196637;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied add-cube-cbrt0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2020064 +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))))