Average Error: 0.3 → 0.3
Time: 37.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + 2 \cdot \log \left(\sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + 2 \cdot \log \left(\sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r61455 = x;
        double r61456 = y;
        double r61457 = r61455 + r61456;
        double r61458 = log(r61457);
        double r61459 = z;
        double r61460 = log(r61459);
        double r61461 = r61458 + r61460;
        double r61462 = t;
        double r61463 = r61461 - r61462;
        double r61464 = a;
        double r61465 = 0.5;
        double r61466 = r61464 - r61465;
        double r61467 = log(r61462);
        double r61468 = r61466 * r61467;
        double r61469 = r61463 + r61468;
        return r61469;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r61470 = x;
        double r61471 = y;
        double r61472 = r61470 + r61471;
        double r61473 = log(r61472);
        double r61474 = 2.0;
        double r61475 = z;
        double r61476 = cbrt(r61475);
        double r61477 = log(r61476);
        double r61478 = r61474 * r61477;
        double r61479 = r61473 + r61478;
        double r61480 = r61479 + r61477;
        double r61481 = t;
        double r61482 = r61480 - r61481;
        double r61483 = a;
        double r61484 = 0.5;
        double r61485 = r61483 - r61484;
        double r61486 = log(r61481);
        double r61487 = r61485 * r61486;
        double r61488 = r61482 + r61487;
        return r61488;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  4. Applied log-prod0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  5. Applied associate-+r+0.3

    \[\leadsto \left(\color{blue}{\left(\left(\log \left(x + y\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]

  6. Simplified0.3

    \[\leadsto \left(\left(\color{blue}{\left(\log \left(x + y\right) + 2 \cdot \log \left(\sqrt[3]{z}\right)\right)} + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  7. Final simplification0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + 2 \cdot \log \left(\sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))