Average Error: 0.3 → 0.3
Time: 38.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\frac{\log \left(x + y\right) \cdot \log \left(x + y\right) - \log z \cdot \log z}{\log \left(x + y\right) - \log z} - t\right) + \left(\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\frac{\log \left(x + y\right) \cdot \log \left(x + y\right) - \log z \cdot \log z}{\log \left(x + y\right) - \log z} - t\right) + \left(\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r192284 = x;
        double r192285 = y;
        double r192286 = r192284 + r192285;
        double r192287 = log(r192286);
        double r192288 = z;
        double r192289 = log(r192288);
        double r192290 = r192287 + r192289;
        double r192291 = t;
        double r192292 = r192290 - r192291;
        double r192293 = a;
        double r192294 = 0.5;
        double r192295 = r192293 - r192294;
        double r192296 = log(r192291);
        double r192297 = r192295 * r192296;
        double r192298 = r192292 + r192297;
        return r192298;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r192299 = x;
        double r192300 = y;
        double r192301 = r192299 + r192300;
        double r192302 = log(r192301);
        double r192303 = r192302 * r192302;
        double r192304 = z;
        double r192305 = log(r192304);
        double r192306 = r192305 * r192305;
        double r192307 = r192303 - r192306;
        double r192308 = r192302 - r192305;
        double r192309 = r192307 / r192308;
        double r192310 = t;
        double r192311 = r192309 - r192310;
        double r192312 = sqrt(r192310);
        double r192313 = log(r192312);
        double r192314 = a;
        double r192315 = 0.5;
        double r192316 = r192314 - r192315;
        double r192317 = r192313 * r192316;
        double r192318 = r192317 + r192317;
        double r192319 = r192311 + r192318;
        return r192319;
}

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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Simplified0.3

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

  7. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \color{blue}{\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)}\right)\]
  8. Using strategy rm

  9. Applied flip-+0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(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))))