Average Error: 0.3 → 0.3
Time: 10.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log \left(x + y\right) + \left(\log z - t\right)\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r413261 = x;
        double r413262 = y;
        double r413263 = r413261 + r413262;
        double r413264 = log(r413263);
        double r413265 = z;
        double r413266 = log(r413265);
        double r413267 = r413264 + r413266;
        double r413268 = t;
        double r413269 = r413267 - r413268;
        double r413270 = a;
        double r413271 = 0.5;
        double r413272 = r413270 - r413271;
        double r413273 = log(r413268);
        double r413274 = r413272 * r413273;
        double r413275 = r413269 + r413274;
        return r413275;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r413276 = x;
        double r413277 = y;
        double r413278 = r413276 + r413277;
        double r413279 = log(r413278);
        double r413280 = z;
        double r413281 = log(r413280);
        double r413282 = t;
        double r413283 = r413281 - r413282;
        double r413284 = r413279 + r413283;
        double r413285 = a;
        double r413286 = 0.5;
        double r413287 = r413285 - r413286;
        double r413288 = log(r413282);
        double r413289 = r413287 * r413288;
        double r413290 = r413284 + r413289;
        return r413290;
}

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. Using strategy rm

  6. Applied associate-+r+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020060 
(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))))