Average Error: 0.1 → 0.2
Time: 4.7s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\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 r166951 = x;
        double r166952 = y;
        double r166953 = cos(r166952);
        double r166954 = r166951 * r166953;
        double r166955 = z;
        double r166956 = sin(r166952);
        double r166957 = r166955 * r166956;
        double r166958 = r166954 + r166957;
        return r166958;
}
↓
double f(double x, double y, double z) {
        double r166959 = x;
        double r166960 = y;
        double r166961 = cos(r166960);
        double r166962 = 2.0;
        double r166963 = pow(r166961, r166962);
        double r166964 = 0.3333333333333333;
        double r166965 = pow(r166963, r166964);
        double r166966 = r166959 * r166965;
        double r166967 = cbrt(r166961);
        double r166968 = r166966 * r166967;
        double r166969 = z;
        double r166970 = sin(r166960);
        double r166971 = r166969 * r166970;
        double r166972 = r166968 + r166971;
        return r166972;
}

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 pow1/316.3

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

  7. Applied pow1/316.2

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))