Average Error: 0.3 → 0.3
Time: 41.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + \log \left(x + y\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + \log \left(x + y\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 r268445 = x;
        double r268446 = y;
        double r268447 = r268445 + r268446;
        double r268448 = log(r268447);
        double r268449 = z;
        double r268450 = log(r268449);
        double r268451 = r268448 + r268450;
        double r268452 = t;
        double r268453 = r268451 - r268452;
        double r268454 = a;
        double r268455 = 0.5;
        double r268456 = r268454 - r268455;
        double r268457 = log(r268452);
        double r268458 = r268456 * r268457;
        double r268459 = r268453 + r268458;
        return r268459;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r268460 = 2.0;
        double r268461 = z;
        double r268462 = cbrt(r268461);
        double r268463 = log(r268462);
        double r268464 = r268460 * r268463;
        double r268465 = x;
        double r268466 = y;
        double r268467 = r268465 + r268466;
        double r268468 = log(r268467);
        double r268469 = r268464 + r268468;
        double r268470 = r268469 + r268463;
        double r268471 = t;
        double r268472 = r268470 - r268471;
        double r268473 = a;
        double r268474 = 0.5;
        double r268475 = r268473 - r268474;
        double r268476 = log(r268471);
        double r268477 = r268475 * r268476;
        double r268478 = r268472 + r268477;
        return r268478;
}

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. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019199 
(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))))