Average Error: 0.1 → 0.2
Time: 13.4s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left(e^{\log \left({\left(\cos y\right)}^{2}\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\left(e^{\log \left({\left(\cos y\right)}^{2}\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r241909 = x;
        double r241910 = y;
        double r241911 = cos(r241910);
        double r241912 = r241909 * r241911;
        double r241913 = z;
        double r241914 = sin(r241910);
        double r241915 = r241913 * r241914;
        double r241916 = r241912 + r241915;
        return r241916;
}
↓
double f(double x, double y, double z) {
        double r241917 = x;
        double r241918 = y;
        double r241919 = cos(r241918);
        double r241920 = 2.0;
        double r241921 = pow(r241919, r241920);
        double r241922 = log(r241921);
        double r241923 = exp(r241922);
        double r241924 = 0.3333333333333333;
        double r241925 = pow(r241923, r241924);
        double r241926 = r241917 * r241925;
        double r241927 = cbrt(r241919);
        double r241928 = r241926 * r241927;
        double r241929 = z;
        double r241930 = sin(r241918);
        double r241931 = r241929 * r241930;
        double r241932 = r241928 + r241931;
        return r241932;
}

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 pow1/316.2

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

  7. Applied pow1/316.2

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

  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-exp-log16.2

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

  12. Applied pow-exp16.2

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))