Average Error: 0.1 → 0.1
Time: 21.0s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log t + \left(x \cdot \log y - \left(y + z\right)\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log t + \left(x \cdot \log y - \left(y + z\right)\right)
double f(double x, double y, double z, double t) {
        double r69599 = x;
        double r69600 = y;
        double r69601 = log(r69600);
        double r69602 = r69599 * r69601;
        double r69603 = r69602 - r69600;
        double r69604 = z;
        double r69605 = r69603 - r69604;
        double r69606 = t;
        double r69607 = log(r69606);
        double r69608 = r69605 + r69607;
        return r69608;
}
↓
double f(double x, double y, double z, double t) {
        double r69609 = t;
        double r69610 = log(r69609);
        double r69611 = x;
        double r69612 = y;
        double r69613 = log(r69612);
        double r69614 = r69611 * r69613;
        double r69615 = z;
        double r69616 = r69612 + r69615;
        double r69617 = r69614 - r69616;
        double r69618 = r69610 + r69617;
        return r69618;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
  2. Using strategy rm

  3. Applied associate--l-0.1

    \[\leadsto \color{blue}{\left(x \cdot \log y - \left(y + z\right)\right)} + \log t\]

  4. Simplified0.1

    \[\leadsto \left(x \cdot \log y - \color{blue}{\left(z + y\right)}\right) + \log t\]

  5. Final simplification0.1

    \[\leadsto \log t + \left(x \cdot \log y - \left(y + z\right)\right)\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))