Average Error: 0.2 → 0.3
Time: 29.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt[3]{z}\right) \cdot 2\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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) + \log \left(\sqrt[3]{z}\right) \cdot 2\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 r64574 = x;
        double r64575 = y;
        double r64576 = r64574 + r64575;
        double r64577 = log(r64576);
        double r64578 = z;
        double r64579 = log(r64578);
        double r64580 = r64577 + r64579;
        double r64581 = t;
        double r64582 = r64580 - r64581;
        double r64583 = a;
        double r64584 = 0.5;
        double r64585 = r64583 - r64584;
        double r64586 = log(r64581);
        double r64587 = r64585 * r64586;
        double r64588 = r64582 + r64587;
        return r64588;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r64589 = x;
        double r64590 = y;
        double r64591 = r64589 + r64590;
        double r64592 = log(r64591);
        double r64593 = z;
        double r64594 = cbrt(r64593);
        double r64595 = log(r64594);
        double r64596 = 2.0;
        double r64597 = r64595 * r64596;
        double r64598 = r64592 + r64597;
        double r64599 = r64598 + r64595;
        double r64600 = t;
        double r64601 = r64599 - r64600;
        double r64602 = a;
        double r64603 = 0.5;
        double r64604 = r64602 - r64603;
        double r64605 = log(r64600);
        double r64606 = r64604 * r64605;
        double r64607 = r64601 + r64606;
        return r64607;
}

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 0.2

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

  3. Applied add-cube-cbrt0.2

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

  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

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019196 
(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))))