Average Error: 0.3 → 0.3
Time: 36.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)\]
\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) + \log z\right) - t\right) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)
double f(double x, double y, double z, double t, double a) {
        double r254333 = x;
        double r254334 = y;
        double r254335 = r254333 + r254334;
        double r254336 = log(r254335);
        double r254337 = z;
        double r254338 = log(r254337);
        double r254339 = r254336 + r254338;
        double r254340 = t;
        double r254341 = r254339 - r254340;
        double r254342 = a;
        double r254343 = 0.5;
        double r254344 = r254342 - r254343;
        double r254345 = log(r254340);
        double r254346 = r254344 * r254345;
        double r254347 = r254341 + r254346;
        return r254347;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r254348 = x;
        double r254349 = y;
        double r254350 = r254348 + r254349;
        double r254351 = log(r254350);
        double r254352 = z;
        double r254353 = log(r254352);
        double r254354 = r254351 + r254353;
        double r254355 = t;
        double r254356 = r254354 - r254355;
        double r254357 = 2.0;
        double r254358 = cbrt(r254355);
        double r254359 = log(r254358);
        double r254360 = r254357 * r254359;
        double r254361 = a;
        double r254362 = 0.5;
        double r254363 = r254361 - r254362;
        double r254364 = r254360 * r254363;
        double r254365 = r254356 + r254364;
        double r254366 = 1.0;
        double r254367 = r254366 / r254355;
        double r254368 = -0.3333333333333333;
        double r254369 = pow(r254367, r254368);
        double r254370 = log(r254369);
        double r254371 = r254363 * r254370;
        double r254372 = r254365 + r254371;
        return r254372;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Simplified0.3

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

  8. Taylor expanded around inf 0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)}\]

  9. Final simplification0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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