Average Error: 0.3 → 0.3
Time: 43.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
double f(double x, double y, double z, double t, double a) {
        double r3278346 = x;
        double r3278347 = y;
        double r3278348 = r3278346 + r3278347;
        double r3278349 = log(r3278348);
        double r3278350 = z;
        double r3278351 = log(r3278350);
        double r3278352 = r3278349 + r3278351;
        double r3278353 = t;
        double r3278354 = r3278352 - r3278353;
        double r3278355 = a;
        double r3278356 = 0.5;
        double r3278357 = r3278355 - r3278356;
        double r3278358 = log(r3278353);
        double r3278359 = r3278357 * r3278358;
        double r3278360 = r3278354 + r3278359;
        return r3278360;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r3278361 = y;
        double r3278362 = x;
        double r3278363 = r3278361 + r3278362;
        double r3278364 = cbrt(r3278363);
        double r3278365 = r3278364 * r3278364;
        double r3278366 = log(r3278365);
        double r3278367 = z;
        double r3278368 = log(r3278367);
        double r3278369 = log(r3278364);
        double r3278370 = r3278368 + r3278369;
        double r3278371 = r3278366 + r3278370;
        double r3278372 = t;
        double r3278373 = r3278371 - r3278372;
        double r3278374 = a;
        double r3278375 = 0.5;
        double r3278376 = r3278374 - r3278375;
        double r3278377 = log(r3278372);
        double r3278378 = r3278376 * r3278377;
        double r3278379 = r3278373 + r3278378;
        return r3278379;
}


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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019101 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))