Average Error: 0.1 → 0.2
Time: 23.1s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r12451039 = x;
        double r12451040 = y;
        double r12451041 = sin(r12451040);
        double r12451042 = r12451039 * r12451041;
        double r12451043 = z;
        double r12451044 = cos(r12451040);
        double r12451045 = r12451043 * r12451044;
        double r12451046 = r12451042 + r12451045;
        return r12451046;
}
↓
double f(double x, double y, double z) {
        double r12451047 = x;
        double r12451048 = y;
        double r12451049 = sin(r12451048);
        double r12451050 = r12451047 * r12451049;
        double r12451051 = z;
        double r12451052 = cos(r12451048);
        double r12451053 = r12451052 * r12451052;
        double r12451054 = 0.3333333333333333;
        double r12451055 = pow(r12451053, r12451054);
        double r12451056 = r12451051 * r12451055;
        double r12451057 = cbrt(r12451052);
        double r12451058 = r12451056 * r12451057;
        double r12451059 = r12451050 + r12451058;
        return r12451059;
}

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 pow1/315.8

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

  7. Applied pow1/315.8

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

  8. Applied pow-prod-down0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))