Average Error: 0.3 → 0.3
Time: 30.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{{t}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{{t}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r59291 = x;
        double r59292 = y;
        double r59293 = r59291 + r59292;
        double r59294 = log(r59293);
        double r59295 = z;
        double r59296 = log(r59295);
        double r59297 = r59294 + r59296;
        double r59298 = t;
        double r59299 = r59297 - r59298;
        double r59300 = a;
        double r59301 = 0.5;
        double r59302 = r59300 - r59301;
        double r59303 = log(r59298);
        double r59304 = r59302 * r59303;
        double r59305 = r59299 + r59304;
        return r59305;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r59306 = x;
        double r59307 = y;
        double r59308 = r59306 + r59307;
        double r59309 = log(r59308);
        double r59310 = z;
        double r59311 = log(r59310);
        double r59312 = r59309 + r59311;
        double r59313 = t;
        double r59314 = r59312 - r59313;
        double r59315 = 2.0;
        double r59316 = cbrt(r59313);
        double r59317 = log(r59316);
        double r59318 = r59315 * r59317;
        double r59319 = a;
        double r59320 = 0.5;
        double r59321 = r59319 - r59320;
        double r59322 = r59318 * r59321;
        double r59323 = 0.6666666666666666;
        double r59324 = pow(r59313, r59323);
        double r59325 = cbrt(r59324);
        double r59326 = cbrt(r59316);
        double r59327 = r59325 * r59326;
        double r59328 = log(r59327);
        double r59329 = r59328 * r59321;
        double r59330 = r59322 + r59329;
        double r59331 = r59314 + r59330;
        return r59331;
}

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-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\color{blue}{\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]

  7. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \color{blue}{\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)}\right)\]
  8. Using strategy rm

  9. Applied add-cube-cbrt0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}\right) \cdot \left(a - 0.5\right)\right)\]

  10. Applied cbrt-prod0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \log \color{blue}{\left(\sqrt[3]{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)} \cdot \left(a - 0.5\right)\right)\]

  11. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \log \left(\color{blue}{\sqrt[3]{{t}^{\frac{2}{3}}}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \left(a - 0.5\right)\right)\]

  12. Final simplification0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{{t}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \left(a - 0.5\right)\right)\]

Reproduce

herbie shell --seed 2019208 
(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))))