Average Error: 0.1 → 0.3
Time: 15.2s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r212927 = x;
        double r212928 = y;
        double r212929 = cos(r212928);
        double r212930 = r212927 * r212929;
        double r212931 = z;
        double r212932 = sin(r212928);
        double r212933 = r212931 * r212932;
        double r212934 = r212930 + r212933;
        return r212934;
}
↓
double f(double x, double y, double z) {
        double r212935 = x;
        double r212936 = y;
        double r212937 = cos(r212936);
        double r212938 = 2.0;
        double r212939 = pow(r212937, r212938);
        double r212940 = 0.6666666666666666;
        double r212941 = pow(r212939, r212940);
        double r212942 = 0.3333333333333333;
        double r212943 = pow(r212939, r212942);
        double r212944 = r212941 * r212943;
        double r212945 = cbrt(r212944);
        double r212946 = r212935 * r212945;
        double r212947 = cbrt(r212937);
        double r212948 = r212946 * r212947;
        double r212949 = z;
        double r212950 = sin(r212936);
        double r212951 = r212949 * r212950;
        double r212952 = r212948 + r212951;
        return r212952;
}

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 cbrt-unprod0.3

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

  7. Simplified0.3

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

  9. Applied add-cube-cbrt0.3

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

  10. Simplified0.3

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

  12. Applied pow1/30.3

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

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))