Average Error: 0.3 → 0.3
Time: 50.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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(y + x\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
double f(double x, double y, double z, double t, double a) {
        double r3617484 = x;
        double r3617485 = y;
        double r3617486 = r3617484 + r3617485;
        double r3617487 = log(r3617486);
        double r3617488 = z;
        double r3617489 = log(r3617488);
        double r3617490 = r3617487 + r3617489;
        double r3617491 = t;
        double r3617492 = r3617490 - r3617491;
        double r3617493 = a;
        double r3617494 = 0.5;
        double r3617495 = r3617493 - r3617494;
        double r3617496 = log(r3617491);
        double r3617497 = r3617495 * r3617496;
        double r3617498 = r3617492 + r3617497;
        return r3617498;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r3617499 = y;
        double r3617500 = x;
        double r3617501 = r3617499 + r3617500;
        double r3617502 = log(r3617501);
        double r3617503 = z;
        double r3617504 = cbrt(r3617503);
        double r3617505 = r3617504 * r3617504;
        double r3617506 = log(r3617505);
        double r3617507 = r3617502 + r3617506;
        double r3617508 = log(r3617504);
        double r3617509 = r3617507 + r3617508;
        double r3617510 = t;
        double r3617511 = r3617509 - r3617510;
        double r3617512 = a;
        double r3617513 = 0.5;
        double r3617514 = r3617512 - r3617513;
        double r3617515 = log(r3617510);
        double r3617516 = r3617514 * r3617515;
        double r3617517 = r3617511 + r3617516;
        return r3617517;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019107 
(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))))