Average Error: 0.1 → 0.2
Time: 25.1s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\sqrt[3]{\sqrt[3]{{\left({\left(\cos y\right)}^{6}\right)}^{3}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\left(\sqrt[3]{\sqrt[3]{{\left({\left(\cos y\right)}^{6}\right)}^{3}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r206592 = x;
        double r206593 = y;
        double r206594 = cos(r206593);
        double r206595 = r206592 * r206594;
        double r206596 = z;
        double r206597 = sin(r206593);
        double r206598 = r206596 * r206597;
        double r206599 = r206595 + r206598;
        return r206599;
}
↓
double f(double x, double y, double z) {
        double r206600 = x;
        double r206601 = y;
        double r206602 = cos(r206601);
        double r206603 = 6.0;
        double r206604 = pow(r206602, r206603);
        double r206605 = 3.0;
        double r206606 = pow(r206604, r206605);
        double r206607 = cbrt(r206606);
        double r206608 = cbrt(r206607);
        double r206609 = 0.3333333333333333;
        double r206610 = pow(r206608, r206609);
        double r206611 = r206600 * r206610;
        double r206612 = cbrt(r206602);
        double r206613 = r206611 * r206612;
        double r206614 = z;
        double r206615 = sin(r206601);
        double r206616 = r206614 * r206615;
        double r206617 = r206613 + r206616;
        return r206617;
}

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

    \[x \cdot \cos y + z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/315.9

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

  7. Applied pow1/315.9

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

  8. Applied pow-prod-down0.2

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

  9. Simplified0.2

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

  11. Applied add-cbrt-cube0.2

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

  12. Simplified0.2

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

  14. Applied add-cbrt-cube0.2

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

  15. Simplified0.2

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

  16. Final simplification0.2

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

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))