Average Error: 0.1 → 0.1
Time: 26.8s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt{t}\right)\right) + \log \left(\sqrt{t}\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt{t}\right)\right) + \log \left(\sqrt{t}\right)
double f(double x, double y, double z, double t) {
        double r4364409 = x;
        double r4364410 = y;
        double r4364411 = log(r4364410);
        double r4364412 = r4364409 * r4364411;
        double r4364413 = r4364412 - r4364410;
        double r4364414 = z;
        double r4364415 = r4364413 - r4364414;
        double r4364416 = t;
        double r4364417 = log(r4364416);
        double r4364418 = r4364415 + r4364417;
        return r4364418;
}
↓
double f(double x, double y, double z, double t) {
        double r4364419 = x;
        double r4364420 = y;
        double r4364421 = log(r4364420);
        double r4364422 = r4364419 * r4364421;
        double r4364423 = r4364422 - r4364420;
        double r4364424 = z;
        double r4364425 = r4364423 - r4364424;
        double r4364426 = t;
        double r4364427 = sqrt(r4364426);
        double r4364428 = log(r4364427);
        double r4364429 = r4364425 + r4364428;
        double r4364430 = r4364429 + r4364428;
        return r4364430;
}

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 add-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied associate-+r+0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))