Average Error: 0.3 → 0.3
Time: 13.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \left(\log \left(\sqrt{z}\right) - t\right)\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \left(\log \left(\sqrt{z}\right) - t\right)\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r403258 = x;
        double r403259 = y;
        double r403260 = r403258 + r403259;
        double r403261 = log(r403260);
        double r403262 = z;
        double r403263 = log(r403262);
        double r403264 = r403261 + r403263;
        double r403265 = t;
        double r403266 = r403264 - r403265;
        double r403267 = a;
        double r403268 = 0.5;
        double r403269 = r403267 - r403268;
        double r403270 = log(r403265);
        double r403271 = r403269 * r403270;
        double r403272 = r403266 + r403271;
        return r403272;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r403273 = x;
        double r403274 = y;
        double r403275 = r403273 + r403274;
        double r403276 = log(r403275);
        double r403277 = z;
        double r403278 = sqrt(r403277);
        double r403279 = log(r403278);
        double r403280 = r403276 + r403279;
        double r403281 = t;
        double r403282 = r403279 - r403281;
        double r403283 = r403280 + r403282;
        double r403284 = a;
        double r403285 = 0.5;
        double r403286 = r403284 - r403285;
        double r403287 = log(r403281);
        double r403288 = r403286 * r403287;
        double r403289 = r403283 + r403288;
        return r403289;
}

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. Using strategy rm

  5. Applied add-sqr-sqrt0.3

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

  6. Applied log-prod0.3

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

  7. Applied associate--l+0.3

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

  8. Applied associate-+r+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020089 
(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))))