Average Error: 0.1 → 0.2
Time: 27.6s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{6}}\right) \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{6}} \cdot \sqrt[3]{\cos y}\right)\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{6}}\right) \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{6}} \cdot \sqrt[3]{\cos y}\right)
double f(double x, double y, double z) {
        double r148445 = x;
        double r148446 = y;
        double r148447 = sin(r148446);
        double r148448 = r148445 * r148447;
        double r148449 = z;
        double r148450 = cos(r148446);
        double r148451 = r148449 * r148450;
        double r148452 = r148448 + r148451;
        return r148452;
}
↓
double f(double x, double y, double z) {
        double r148453 = x;
        double r148454 = y;
        double r148455 = sin(r148454);
        double r148456 = r148453 * r148455;
        double r148457 = z;
        double r148458 = cos(r148454);
        double r148459 = 2.0;
        double r148460 = pow(r148458, r148459);
        double r148461 = 0.16666666666666666;
        double r148462 = pow(r148460, r148461);
        double r148463 = r148457 * r148462;
        double r148464 = cbrt(r148458);
        double r148465 = r148462 * r148464;
        double r148466 = r148463 * r148465;
        double r148467 = r148456 + r148466;
        return r148467;
}

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 pow1/315.9

    \[\leadsto x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y}\]

  7. Applied pow1/315.9

    \[\leadsto x \cdot \sin y + \left(z \cdot \left(\color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}} \cdot {\left(\cos y\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y}\]

  8. Applied pow-prod-down0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot \color{blue}{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}\]

  9. Simplified0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot {\color{blue}{\left({\left(\cos y\right)}^{2}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
  10. Using strategy rm

  11. Applied sqr-pow0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot \color{blue}{\left({\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{\frac{1}{3}}{2}\right)} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{\frac{1}{3}}{2}\right)}\right)}\right) \cdot \sqrt[3]{\cos y}\]

  12. Applied associate-*r*0.2

    \[\leadsto x \cdot \sin y + \color{blue}{\left(\left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{\frac{1}{3}}{2}\right)}\right) \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{\frac{1}{3}}{2}\right)}\right)} \cdot \sqrt[3]{\cos y}\]

  13. Simplified0.2

    \[\leadsto x \cdot \sin y + \left(\color{blue}{\left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{6}}\right)} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{\frac{1}{3}}{2}\right)}\right) \cdot \sqrt[3]{\cos y}\]
  14. Using strategy rm

  15. Applied associate-*l*0.2

    \[\leadsto x \cdot \sin y + \color{blue}{\left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{6}}\right) \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{\frac{1}{3}}{2}\right)} \cdot \sqrt[3]{\cos y}\right)}\]

  16. Simplified0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{6}}\right) \cdot \color{blue}{\left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{6}} \cdot \sqrt[3]{\cos y}\right)}\]

  17. Final simplification0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{6}}\right) \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{6}} \cdot \sqrt[3]{\cos y}\right)\]

Reproduce

herbie shell --seed 2019306 
(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))))