Average Error: 0.1 → 0.2
Time: 16.7s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\sqrt[3]{{\left({\left({\left(\cos y\right)}^{2}\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\left(\sqrt[3]{{\left({\left({\left(\cos y\right)}^{2}\right)}^{\left(\sqrt{3}\right)}\right)}^{\left(\sqrt{3}\right)}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r181254 = x;
        double r181255 = y;
        double r181256 = cos(r181255);
        double r181257 = r181254 * r181256;
        double r181258 = z;
        double r181259 = sin(r181255);
        double r181260 = r181258 * r181259;
        double r181261 = r181257 + r181260;
        return r181261;
}
↓
double f(double x, double y, double z) {
        double r181262 = x;
        double r181263 = y;
        double r181264 = cos(r181263);
        double r181265 = 2.0;
        double r181266 = pow(r181264, r181265);
        double r181267 = 3.0;
        double r181268 = sqrt(r181267);
        double r181269 = pow(r181266, r181268);
        double r181270 = pow(r181269, r181268);
        double r181271 = cbrt(r181270);
        double r181272 = 0.3333333333333333;
        double r181273 = pow(r181271, r181272);
        double r181274 = r181262 * r181273;
        double r181275 = cbrt(r181264);
        double r181276 = r181274 * r181275;
        double r181277 = z;
        double r181278 = sin(r181263);
        double r181279 = r181277 * r181278;
        double r181280 = r181276 + r181279;
        return r181280;
}

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 pow1/315.6

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

  7. Applied pow1/315.6

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

  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

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

  14. Applied add-sqr-sqrt0.2

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

  15. Applied pow-unpow0.2

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

  16. Final simplification0.2

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

Reproduce

herbie shell --seed 2019209 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))