Average Error: 0.1 → 0.2
Time: 24.0s
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 r118737 = x;
        double r118738 = y;
        double r118739 = sin(r118738);
        double r118740 = r118737 * r118739;
        double r118741 = z;
        double r118742 = cos(r118738);
        double r118743 = r118741 * r118742;
        double r118744 = r118740 + r118743;
        return r118744;
}
↓
double f(double x, double y, double z) {
        double r118745 = x;
        double r118746 = y;
        double r118747 = sin(r118746);
        double r118748 = r118745 * r118747;
        double r118749 = z;
        double r118750 = cos(r118746);
        double r118751 = 2.0;
        double r118752 = pow(r118750, r118751);
        double r118753 = 0.16666666666666666;
        double r118754 = pow(r118752, r118753);
        double r118755 = r118749 * r118754;
        double r118756 = cbrt(r118750);
        double r118757 = r118754 * r118756;
        double r118758 = r118755 * r118757;
        double r118759 = r118748 + r118758;
        return r118759;
}

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 +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))))