Average Error: 0.3 → 0.3
Time: 22.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt{x + y}\right) + \frac{{\left(\log \left(\sqrt{x + y}\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(\sqrt{x + y}\right)\right) + \log \left(\sqrt{x + y}\right) \cdot \log \left(\sqrt{x + y}\right)}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(\sqrt{x + y}\right) + \frac{{\left(\log \left(\sqrt{x + y}\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(\sqrt{x + y}\right)\right) + \log \left(\sqrt{x + y}\right) \cdot \log \left(\sqrt{x + y}\right)}\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r319239 = x;
        double r319240 = y;
        double r319241 = r319239 + r319240;
        double r319242 = log(r319241);
        double r319243 = z;
        double r319244 = log(r319243);
        double r319245 = r319242 + r319244;
        double r319246 = t;
        double r319247 = r319245 - r319246;
        double r319248 = a;
        double r319249 = 0.5;
        double r319250 = r319248 - r319249;
        double r319251 = log(r319246);
        double r319252 = r319250 * r319251;
        double r319253 = r319247 + r319252;
        return r319253;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r319254 = x;
        double r319255 = y;
        double r319256 = r319254 + r319255;
        double r319257 = sqrt(r319256);
        double r319258 = log(r319257);
        double r319259 = 3.0;
        double r319260 = pow(r319258, r319259);
        double r319261 = z;
        double r319262 = log(r319261);
        double r319263 = pow(r319262, r319259);
        double r319264 = r319260 + r319263;
        double r319265 = r319262 - r319258;
        double r319266 = r319262 * r319265;
        double r319267 = r319258 * r319258;
        double r319268 = r319266 + r319267;
        double r319269 = r319264 / r319268;
        double r319270 = r319258 + r319269;
        double r319271 = t;
        double r319272 = r319270 - r319271;
        double r319273 = a;
        double r319274 = 0.5;
        double r319275 = r319273 - r319274;
        double r319276 = log(r319271);
        double r319277 = r319275 * r319276;
        double r319278 = r319272 + r319277;
        return r319278;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  7. Applied flip3-+0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 1978988140 
(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))))