Average Error: 0.1 → 0.3
Time: 5.0s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right)}^{\frac{1}{3}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\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 r213005 = x;
        double r213006 = y;
        double r213007 = cos(r213006);
        double r213008 = r213005 * r213007;
        double r213009 = z;
        double r213010 = sin(r213006);
        double r213011 = r213009 * r213010;
        double r213012 = r213008 - r213011;
        return r213012;
}
↓
double f(double x, double y, double z) {
        double r213013 = x;
        double r213014 = y;
        double r213015 = cos(r213014);
        double r213016 = 2.0;
        double r213017 = pow(r213015, r213016);
        double r213018 = 0.6666666666666666;
        double r213019 = pow(r213017, r213018);
        double r213020 = 0.3333333333333333;
        double r213021 = pow(r213017, r213020);
        double r213022 = r213019 * r213021;
        double r213023 = pow(r213022, r213020);
        double r213024 = r213013 * r213023;
        double r213025 = cbrt(r213015);
        double r213026 = exp(r213025);
        double r213027 = log(r213026);
        double r213028 = r213024 * r213027;
        double r213029 = z;
        double r213030 = sin(r213014);
        double r213031 = r213029 * r213030;
        double r213032 = r213028 - r213031;
        return r213032;
}

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-cube-cbrt0.3

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

  12. Simplified0.2

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

  13. Simplified0.2

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

  15. Applied add-log-exp0.3

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

  16. Final simplification0.3

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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))))