Average Error: 0.1 → 0.3
Time: 5.3s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + z \cdot \left(\left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + z \cdot \left(\left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)
double f(double x, double y, double z) {
        double r185940 = x;
        double r185941 = y;
        double r185942 = sin(r185941);
        double r185943 = r185940 * r185942;
        double r185944 = z;
        double r185945 = cos(r185941);
        double r185946 = r185944 * r185945;
        double r185947 = r185943 + r185946;
        return r185947;
}
↓
double f(double x, double y, double z) {
        double r185948 = x;
        double r185949 = y;
        double r185950 = sin(r185949);
        double r185951 = r185948 * r185950;
        double r185952 = z;
        double r185953 = cos(r185949);
        double r185954 = 2.0;
        double r185955 = pow(r185953, r185954);
        double r185956 = 0.3333333333333333;
        double r185957 = pow(r185955, r185956);
        double r185958 = cbrt(r185953);
        double r185959 = pow(r185958, r185954);
        double r185960 = cbrt(r185959);
        double r185961 = r185957 * r185960;
        double r185962 = cbrt(r185958);
        double r185963 = r185961 * r185962;
        double r185964 = r185952 * r185963;
        double r185965 = r185951 + r185964;
        return r185965;
}

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 cbrt-unprod0.3

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

  7. Simplified0.3

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

  9. Applied associate-*l*0.3

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

  11. Applied add-cube-cbrt0.3

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

  12. Applied cbrt-prod0.3

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

  13. Applied associate-*r*0.3

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

  14. Simplified0.3

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

  15. Final simplification0.3

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

Reproduce

herbie shell --seed 2020089 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))