Average Error: 0.3 → 0.3
Time: 33.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) + \left(\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right) + \log t \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(y + x\right) + \left(\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right) + \log t \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r20461265 = x;
        double r20461266 = y;
        double r20461267 = r20461265 + r20461266;
        double r20461268 = log(r20461267);
        double r20461269 = z;
        double r20461270 = log(r20461269);
        double r20461271 = r20461268 + r20461270;
        double r20461272 = t;
        double r20461273 = r20461271 - r20461272;
        double r20461274 = a;
        double r20461275 = 0.5;
        double r20461276 = r20461274 - r20461275;
        double r20461277 = log(r20461272);
        double r20461278 = r20461276 * r20461277;
        double r20461279 = r20461273 + r20461278;
        return r20461279;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r20461280 = y;
        double r20461281 = x;
        double r20461282 = r20461280 + r20461281;
        double r20461283 = log(r20461282);
        double r20461284 = z;
        double r20461285 = cbrt(r20461284);
        double r20461286 = r20461285 * r20461285;
        double r20461287 = log(r20461286);
        double r20461288 = log(r20461285);
        double r20461289 = t;
        double r20461290 = r20461288 - r20461289;
        double r20461291 = r20461287 + r20461290;
        double r20461292 = log(r20461289);
        double r20461293 = a;
        double r20461294 = 0.5;
        double r20461295 = r20461293 - r20461294;
        double r20461296 = r20461292 * r20461295;
        double r20461297 = r20461291 + r20461296;
        double r20461298 = r20461283 + r20461297;
        return r20461298;
}

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 add-cube-cbrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied associate--l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))