Average Error: 0.1 → 0.3
Time: 4.7s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r265966 = x;
        double r265967 = y;
        double r265968 = sin(r265967);
        double r265969 = r265966 * r265968;
        double r265970 = z;
        double r265971 = cos(r265967);
        double r265972 = r265970 * r265971;
        double r265973 = r265969 + r265972;
        return r265973;
}
↓
double f(double x, double y, double z) {
        double r265974 = x;
        double r265975 = y;
        double r265976 = sin(r265975);
        double r265977 = r265974 * r265976;
        double r265978 = z;
        double r265979 = cos(r265975);
        double r265980 = 2.0;
        double r265981 = pow(r265979, r265980);
        double r265982 = cbrt(r265981);
        double r265983 = r265978 * r265982;
        double r265984 = cbrt(r265979);
        double r265985 = r265983 * r265984;
        double r265986 = r265977 + r265985;
        return r265986;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020036 
(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))))