Average Error: 0.1 → 0.4
Time: 16.4s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \sqrt[3]{\log \left(e^{\cos y \cdot \cos y}\right)}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \sqrt[3]{\log \left(e^{\cos y \cdot \cos y}\right)}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r9624625 = x;
        double r9624626 = y;
        double r9624627 = sin(r9624626);
        double r9624628 = r9624625 * r9624627;
        double r9624629 = z;
        double r9624630 = cos(r9624626);
        double r9624631 = r9624629 * r9624630;
        double r9624632 = r9624628 + r9624631;
        return r9624632;
}
↓
double f(double x, double y, double z) {
        double r9624633 = x;
        double r9624634 = y;
        double r9624635 = sin(r9624634);
        double r9624636 = r9624633 * r9624635;
        double r9624637 = z;
        double r9624638 = cos(r9624634);
        double r9624639 = r9624638 * r9624638;
        double r9624640 = exp(r9624639);
        double r9624641 = log(r9624640);
        double r9624642 = cbrt(r9624641);
        double r9624643 = r9624637 * r9624642;
        double r9624644 = cbrt(r9624638);
        double r9624645 = r9624643 * r9624644;
        double r9624646 = r9624636 + r9624645;
        return r9624646;
}

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 cbrt-unprod0.3

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

  8. Applied add-log-exp0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))