Average Error: 0.3 → 0.3
Time: 28.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]
\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) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r1550415 = x;
        double r1550416 = y;
        double r1550417 = r1550415 + r1550416;
        double r1550418 = log(r1550417);
        double r1550419 = z;
        double r1550420 = log(r1550419);
        double r1550421 = r1550418 + r1550420;
        double r1550422 = t;
        double r1550423 = r1550421 - r1550422;
        double r1550424 = a;
        double r1550425 = 0.5;
        double r1550426 = r1550424 - r1550425;
        double r1550427 = log(r1550422);
        double r1550428 = r1550426 * r1550427;
        double r1550429 = r1550423 + r1550428;
        return r1550429;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1550430 = x;
        double r1550431 = y;
        double r1550432 = r1550430 + r1550431;
        double r1550433 = log(r1550432);
        double r1550434 = z;
        double r1550435 = cbrt(r1550434);
        double r1550436 = log(r1550435);
        double r1550437 = r1550436 + r1550436;
        double r1550438 = r1550433 + r1550437;
        double r1550439 = r1550438 + r1550436;
        double r1550440 = t;
        double r1550441 = r1550439 - r1550440;
        double r1550442 = log(r1550440);
        double r1550443 = a;
        double r1550444 = 0.5;
        double r1550445 = r1550443 - r1550444;
        double r1550446 = r1550442 * r1550445;
        double r1550447 = r1550441 + r1550446;
        return r1550447;
}

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

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019152 
(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))))