Average Error: 0.1 → 0.1
Time: 23.2s
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 r4185541 = x;
        double r4185542 = y;
        double r4185543 = log(r4185542);
        double r4185544 = r4185541 * r4185543;
        double r4185545 = r4185544 - r4185542;
        double r4185546 = z;
        double r4185547 = r4185545 - r4185546;
        double r4185548 = t;
        double r4185549 = log(r4185548);
        double r4185550 = r4185547 + r4185549;
        return r4185550;
}
↓
double f(double x, double y, double z, double t) {
        double r4185551 = x;
        double r4185552 = y;
        double r4185553 = log(r4185552);
        double r4185554 = r4185551 * r4185553;
        double r4185555 = r4185554 - r4185552;
        double r4185556 = z;
        double r4185557 = r4185555 - r4185556;
        double r4185558 = t;
        double r4185559 = sqrt(r4185558);
        double r4185560 = log(r4185559);
        double r4185561 = r4185557 + r4185560;
        double r4185562 = r4185561 + r4185560;
        return r4185562;
}

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 2019174 +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)))