Average Error: 0.1 → 0.2
Time: 18.0s
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 r9507011 = x;
        double r9507012 = y;
        double r9507013 = cos(r9507012);
        double r9507014 = r9507011 * r9507013;
        double r9507015 = z;
        double r9507016 = sin(r9507012);
        double r9507017 = r9507015 * r9507016;
        double r9507018 = r9507014 + r9507017;
        return r9507018;
}
↓
double f(double x, double y, double z) {
        double r9507019 = y;
        double r9507020 = cos(r9507019);
        double r9507021 = cbrt(r9507020);
        double r9507022 = r9507020 * r9507020;
        double r9507023 = 0.3333333333333333;
        double r9507024 = pow(r9507022, r9507023);
        double r9507025 = x;
        double r9507026 = r9507024 * r9507025;
        double r9507027 = r9507021 * r9507026;
        double r9507028 = z;
        double r9507029 = sin(r9507019);
        double r9507030 = r9507028 * r9507029;
        double r9507031 = r9507027 + r9507030;
        return r9507031;
}

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 pow1/316.2

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

  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. 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 2019192 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))