Average Error: 0.1 → 0.2
Time: 5.2s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\cos y}\right) + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{\cos y}\right) + z \cdot \sin y
double f(double x, double y, double z) {
        double r160840 = x;
        double r160841 = y;
        double r160842 = cos(r160841);
        double r160843 = r160840 * r160842;
        double r160844 = z;
        double r160845 = sin(r160841);
        double r160846 = r160844 * r160845;
        double r160847 = r160843 + r160846;
        return r160847;
}
↓
double f(double x, double y, double z) {
        double r160848 = x;
        double r160849 = y;
        double r160850 = cos(r160849);
        double r160851 = 2.0;
        double r160852 = pow(r160850, r160851);
        double r160853 = 0.3333333333333333;
        double r160854 = pow(r160852, r160853);
        double r160855 = cbrt(r160850);
        double r160856 = r160854 * r160855;
        double r160857 = r160848 * r160856;
        double r160858 = z;
        double r160859 = sin(r160849);
        double r160860 = r160858 * r160859;
        double r160861 = r160857 + r160860;
        return r160861;
}

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 pow1/316.1

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

  7. Applied pow1/316.0

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

  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 associate-*l*0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))