Average Error: 0.1 → 0.2
Time: 14.3s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(\sqrt[3]{\cos y} \cdot z\right) \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(\sqrt[3]{\cos y} \cdot z\right) \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}
double f(double x, double y, double z) {
        double r3976927 = x;
        double r3976928 = y;
        double r3976929 = sin(r3976928);
        double r3976930 = r3976927 * r3976929;
        double r3976931 = z;
        double r3976932 = cos(r3976928);
        double r3976933 = r3976931 * r3976932;
        double r3976934 = r3976930 + r3976933;
        return r3976934;
}
↓
double f(double x, double y, double z) {
        double r3976935 = x;
        double r3976936 = y;
        double r3976937 = sin(r3976936);
        double r3976938 = r3976935 * r3976937;
        double r3976939 = cos(r3976936);
        double r3976940 = cbrt(r3976939);
        double r3976941 = z;
        double r3976942 = r3976940 * r3976941;
        double r3976943 = r3976939 * r3976939;
        double r3976944 = 0.3333333333333333;
        double r3976945 = pow(r3976943, r3976944);
        double r3976946 = r3976942 * r3976945;
        double r3976947 = r3976938 + r3976946;
        return r3976947;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.0

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

  7. Applied pow1/316.0

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

  8. Applied pow-prod-down0.2

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

  10. Applied pow10.2

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

  11. Applied pow10.2

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

  12. Applied pow-prod-down0.2

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

  13. Simplified0.3

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

  15. Applied pow1/30.2

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

  16. Final simplification0.2

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))