Average Error: 0.3 → 0.3
Time: 36.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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 r1028555 = x;
        double r1028556 = y;
        double r1028557 = r1028555 + r1028556;
        double r1028558 = log(r1028557);
        double r1028559 = z;
        double r1028560 = log(r1028559);
        double r1028561 = r1028558 + r1028560;
        double r1028562 = t;
        double r1028563 = r1028561 - r1028562;
        double r1028564 = a;
        double r1028565 = 0.5;
        double r1028566 = r1028564 - r1028565;
        double r1028567 = log(r1028562);
        double r1028568 = r1028566 * r1028567;
        double r1028569 = r1028563 + r1028568;
        return r1028569;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1028570 = y;
        double r1028571 = x;
        double r1028572 = r1028570 + r1028571;
        double r1028573 = log(r1028572);
        double r1028574 = z;
        double r1028575 = cbrt(r1028574);
        double r1028576 = r1028575 * r1028575;
        double r1028577 = log(r1028576);
        double r1028578 = r1028573 + r1028577;
        double r1028579 = log(r1028575);
        double r1028580 = r1028578 + r1028579;
        double r1028581 = t;
        double r1028582 = r1028580 - r1028581;
        double r1028583 = a;
        double r1028584 = 0.5;
        double r1028585 = r1028583 - r1028584;
        double r1028586 = log(r1028581);
        double r1028587 = r1028585 * r1028586;
        double r1028588 = r1028582 + r1028587;
        return r1028588;
}

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 2019152 +o rules:numerics
(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))))