Average Error: 0.1 → 0.2
Time: 4.9s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r190932 = x;
        double r190933 = y;
        double r190934 = cos(r190933);
        double r190935 = r190932 * r190934;
        double r190936 = z;
        double r190937 = sin(r190933);
        double r190938 = r190936 * r190937;
        double r190939 = r190935 - r190938;
        return r190939;
}
↓
double f(double x, double y, double z) {
        double r190940 = x;
        double r190941 = y;
        double r190942 = cos(r190941);
        double r190943 = 2.0;
        double r190944 = pow(r190942, r190943);
        double r190945 = 0.3333333333333333;
        double r190946 = pow(r190944, r190945);
        double r190947 = r190940 * r190946;
        double r190948 = cbrt(r190942);
        double r190949 = exp(r190948);
        double r190950 = log(r190949);
        double r190951 = r190947 * r190950;
        double r190952 = z;
        double r190953 = sin(r190941);
        double r190954 = r190952 * r190953;
        double r190955 = r190951 - r190954;
        return r190955;
}

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 pow1/316.5

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

  7. Applied pow1/316.5

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

  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-log-exp0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))