Average Error: 0.1 → 0.1
Time: 6.6s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \log \left(\sqrt{y}\right) + x \cdot \log \left(\sqrt{y}\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \log \left(\sqrt{y}\right) + x \cdot \log \left(\sqrt{y}\right)\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r104457 = x;
        double r104458 = y;
        double r104459 = log(r104458);
        double r104460 = r104457 * r104459;
        double r104461 = r104460 - r104458;
        double r104462 = z;
        double r104463 = r104461 - r104462;
        double r104464 = t;
        double r104465 = log(r104464);
        double r104466 = r104463 + r104465;
        return r104466;
}
↓
double f(double x, double y, double z, double t) {
        double r104467 = x;
        double r104468 = y;
        double r104469 = sqrt(r104468);
        double r104470 = log(r104469);
        double r104471 = r104467 * r104470;
        double r104472 = r104471 + r104471;
        double r104473 = r104472 - r104468;
        double r104474 = z;
        double r104475 = r104473 - r104474;
        double r104476 = t;
        double r104477 = log(r104476);
        double r104478 = r104475 + r104477;
        return r104478;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))