Average Error: 0.1 → 0.3
Time: 5.3s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}} + z \cdot \sin y
double f(double x, double y, double z) {
        double r236956 = x;
        double r236957 = y;
        double r236958 = cos(r236957);
        double r236959 = r236956 * r236958;
        double r236960 = z;
        double r236961 = sin(r236957);
        double r236962 = r236960 * r236961;
        double r236963 = r236959 + r236962;
        return r236963;
}
↓
double f(double x, double y, double z) {
        double r236964 = x;
        double r236965 = y;
        double r236966 = cos(r236965);
        double r236967 = 2.0;
        double r236968 = pow(r236966, r236967);
        double r236969 = 0.3333333333333333;
        double r236970 = pow(r236968, r236969);
        double r236971 = r236964 * r236970;
        double r236972 = cbrt(r236966);
        double r236973 = pow(r236972, r236967);
        double r236974 = cbrt(r236973);
        double r236975 = r236971 * r236974;
        double r236976 = cbrt(r236972);
        double r236977 = r236975 * r236976;
        double r236978 = z;
        double r236979 = sin(r236965);
        double r236980 = r236978 * r236979;
        double r236981 = r236977 + r236980;
        return r236981;
}

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

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

  10. Applied cbrt-prod0.3

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

  11. Applied associate-*r*0.3

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

  12. Simplified0.3

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

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))