Average Error: 0.1 → 0.2
Time: 24.1s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + z \cdot \sqrt[3]{{\left(\cos y\right)}^{3}}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + z \cdot \sqrt[3]{{\left(\cos y\right)}^{3}}
double f(double x, double y, double z) {
        double r156615 = x;
        double r156616 = y;
        double r156617 = sin(r156616);
        double r156618 = r156615 * r156617;
        double r156619 = z;
        double r156620 = cos(r156616);
        double r156621 = r156619 * r156620;
        double r156622 = r156618 + r156621;
        return r156622;
}
↓
double f(double x, double y, double z) {
        double r156623 = x;
        double r156624 = y;
        double r156625 = sin(r156624);
        double r156626 = r156623 * r156625;
        double r156627 = z;
        double r156628 = cos(r156624);
        double r156629 = 3.0;
        double r156630 = pow(r156628, r156629);
        double r156631 = cbrt(r156630);
        double r156632 = r156627 * r156631;
        double r156633 = r156626 + r156632;
        return r156633;
}

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. Simplified0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{\color{blue}{{\left(\cos y\right)}^{2}}}\right) \cdot \sqrt[3]{\cos y}\]
  8. Using strategy rm

  9. Applied associate-*l*0.3

    \[\leadsto x \cdot \sin y + \color{blue}{z \cdot \left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot \sqrt[3]{\cos y}\right)}\]
  10. Using strategy rm

  11. Applied cbrt-unprod0.2

    \[\leadsto x \cdot \sin y + z \cdot \color{blue}{\sqrt[3]{{\left(\cos y\right)}^{2} \cdot \cos y}}\]

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019325 
(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))))