Average Error: 0.3 → 0.3
Time: 37.3s
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 r19530520 = x;
        double r19530521 = y;
        double r19530522 = r19530520 + r19530521;
        double r19530523 = log(r19530522);
        double r19530524 = z;
        double r19530525 = log(r19530524);
        double r19530526 = r19530523 + r19530525;
        double r19530527 = t;
        double r19530528 = r19530526 - r19530527;
        double r19530529 = a;
        double r19530530 = 0.5;
        double r19530531 = r19530529 - r19530530;
        double r19530532 = log(r19530527);
        double r19530533 = r19530531 * r19530532;
        double r19530534 = r19530528 + r19530533;
        return r19530534;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r19530535 = y;
        double r19530536 = x;
        double r19530537 = r19530535 + r19530536;
        double r19530538 = log(r19530537);
        double r19530539 = z;
        double r19530540 = cbrt(r19530539);
        double r19530541 = r19530540 * r19530540;
        double r19530542 = log(r19530541);
        double r19530543 = r19530538 + r19530542;
        double r19530544 = log(r19530540);
        double r19530545 = r19530543 + r19530544;
        double r19530546 = t;
        double r19530547 = r19530545 - r19530546;
        double r19530548 = a;
        double r19530549 = 0.5;
        double r19530550 = r19530548 - r19530549;
        double r19530551 = log(r19530546);
        double r19530552 = r19530550 * r19530551;
        double r19530553 = r19530547 + r19530552;
        return r19530553;
}

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

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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 2019171 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))