Average Error: 0.3 → 0.3
Time: 10.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r353333 = x;
        double r353334 = y;
        double r353335 = r353333 + r353334;
        double r353336 = log(r353335);
        double r353337 = z;
        double r353338 = log(r353337);
        double r353339 = r353336 + r353338;
        double r353340 = t;
        double r353341 = r353339 - r353340;
        double r353342 = a;
        double r353343 = 0.5;
        double r353344 = r353342 - r353343;
        double r353345 = log(r353340);
        double r353346 = r353344 * r353345;
        double r353347 = r353341 + r353346;
        return r353347;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r353348 = x;
        double r353349 = y;
        double r353350 = r353348 + r353349;
        double r353351 = log(r353350);
        double r353352 = 3.0;
        double r353353 = pow(r353351, r353352);
        double r353354 = z;
        double r353355 = log(r353354);
        double r353356 = pow(r353355, r353352);
        double r353357 = r353353 + r353356;
        double r353358 = r353355 - r353351;
        double r353359 = r353355 * r353358;
        double r353360 = r353351 * r353351;
        double r353361 = r353359 + r353360;
        double r353362 = r353357 / r353361;
        double r353363 = t;
        double r353364 = r353362 - r353363;
        double r353365 = a;
        double r353366 = 0.5;
        double r353367 = r353365 - r353366;
        double r353368 = log(r353363);
        double r353369 = r353367 * r353368;
        double r353370 = r353364 + r353369;
        return r353370;
}

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 flip3-+0.3

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

  4. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020025 
(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))))