Average Error: 0.3 → 0.3
Time: 18.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r178259 = x;
        double r178260 = y;
        double r178261 = r178259 + r178260;
        double r178262 = log(r178261);
        double r178263 = z;
        double r178264 = log(r178263);
        double r178265 = r178262 + r178264;
        double r178266 = t;
        double r178267 = r178265 - r178266;
        double r178268 = a;
        double r178269 = 0.5;
        double r178270 = r178268 - r178269;
        double r178271 = log(r178266);
        double r178272 = r178270 * r178271;
        double r178273 = r178267 + r178272;
        return r178273;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r178274 = x;
        double r178275 = y;
        double r178276 = r178274 + r178275;
        double r178277 = log(r178276);
        double r178278 = z;
        double r178279 = log(r178278);
        double r178280 = t;
        double r178281 = r178279 - r178280;
        double r178282 = a;
        double r178283 = 0.5;
        double r178284 = r178282 - r178283;
        double r178285 = log(r178280);
        double r178286 = r178284 * r178285;
        double r178287 = r178281 + r178286;
        double r178288 = r178277 + r178287;
        return r178288;
}

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 associate--l+0.3

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

  4. Applied associate-+l+0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020045 
(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))))