Average Error: 0.3 → 0.3
Time: 37.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\frac{\log \left(x + y\right) \cdot \log \left(x + y\right) - \log z \cdot \log z}{\log \left(x + y\right) - \log z} - t\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right)\]
\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(\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r61290 = x;
        double r61291 = y;
        double r61292 = r61290 + r61291;
        double r61293 = log(r61292);
        double r61294 = z;
        double r61295 = log(r61294);
        double r61296 = r61293 + r61295;
        double r61297 = t;
        double r61298 = r61296 - r61297;
        double r61299 = a;
        double r61300 = 0.5;
        double r61301 = r61299 - r61300;
        double r61302 = log(r61297);
        double r61303 = r61301 * r61302;
        double r61304 = r61298 + r61303;
        return r61304;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r61305 = x;
        double r61306 = y;
        double r61307 = r61305 + r61306;
        double r61308 = log(r61307);
        double r61309 = r61308 * r61308;
        double r61310 = z;
        double r61311 = log(r61310);
        double r61312 = r61311 * r61311;
        double r61313 = r61309 - r61312;
        double r61314 = r61308 - r61311;
        double r61315 = r61313 / r61314;
        double r61316 = t;
        double r61317 = r61315 - r61316;
        double r61318 = a;
        double r61319 = 0.5;
        double r61320 = r61318 - r61319;
        double r61321 = sqrt(r61316);
        double r61322 = log(r61321);
        double r61323 = r61320 * r61322;
        double r61324 = r61323 + r61323;
        double r61325 = r61317 + r61324;
        return r61325;
}

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

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. Using strategy rm

  7. Applied flip-+0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))