Average Error: 0.1 → 0.5
Time: 4.9s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r201784 = x;
        double r201785 = y;
        double r201786 = sin(r201785);
        double r201787 = r201784 * r201786;
        double r201788 = z;
        double r201789 = cos(r201785);
        double r201790 = r201788 * r201789;
        double r201791 = r201787 + r201790;
        return r201791;
}
↓
double f(double x, double y, double z) {
        double r201792 = x;
        double r201793 = y;
        double r201794 = sin(r201793);
        double r201795 = r201792 * r201794;
        double r201796 = z;
        double r201797 = cos(r201793);
        double r201798 = cbrt(r201797);
        double r201799 = cbrt(r201798);
        double r201800 = r201799 * r201799;
        double r201801 = r201800 * r201799;
        double r201802 = r201801 * r201798;
        double r201803 = r201796 * r201802;
        double r201804 = r201803 * r201798;
        double r201805 = r201795 + r201804;
        return r201805;
}

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

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2020064 
(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))))