Average Error: 0.1 → 0.2
Time: 19.2s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot x\right) + z \cdot \sin y
double f(double x, double y, double z) {
        double r9475952 = x;
        double r9475953 = y;
        double r9475954 = cos(r9475953);
        double r9475955 = r9475952 * r9475954;
        double r9475956 = z;
        double r9475957 = sin(r9475953);
        double r9475958 = r9475956 * r9475957;
        double r9475959 = r9475955 + r9475958;
        return r9475959;
}
↓
double f(double x, double y, double z) {
        double r9475960 = y;
        double r9475961 = cos(r9475960);
        double r9475962 = cbrt(r9475961);
        double r9475963 = r9475961 * r9475961;
        double r9475964 = 0.3333333333333333;
        double r9475965 = pow(r9475963, r9475964);
        double r9475966 = x;
        double r9475967 = r9475965 * r9475966;
        double r9475968 = r9475962 * r9475967;
        double r9475969 = z;
        double r9475970 = sin(r9475960);
        double r9475971 = r9475969 * r9475970;
        double r9475972 = r9475968 + r9475971;
        return r9475972;
}

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 pow1/316.4

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

  7. Applied pow1/316.4

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))