Average Error: 0.2 → 0.3
Time: 37.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log \left(\sqrt[3]{y + x}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log \left(\sqrt[3]{y + x}\right) + \left(\log t \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r1479313 = x;
        double r1479314 = y;
        double r1479315 = r1479313 + r1479314;
        double r1479316 = log(r1479315);
        double r1479317 = z;
        double r1479318 = log(r1479317);
        double r1479319 = r1479316 + r1479318;
        double r1479320 = t;
        double r1479321 = r1479319 - r1479320;
        double r1479322 = a;
        double r1479323 = 0.5;
        double r1479324 = r1479322 - r1479323;
        double r1479325 = log(r1479320);
        double r1479326 = r1479324 * r1479325;
        double r1479327 = r1479321 + r1479326;
        return r1479327;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1479328 = y;
        double r1479329 = x;
        double r1479330 = r1479328 + r1479329;
        double r1479331 = cbrt(r1479330);
        double r1479332 = r1479331 * r1479331;
        double r1479333 = log(r1479332);
        double r1479334 = log(r1479331);
        double r1479335 = t;
        double r1479336 = log(r1479335);
        double r1479337 = a;
        double r1479338 = 0.5;
        double r1479339 = r1479337 - r1479338;
        double r1479340 = r1479336 * r1479339;
        double r1479341 = z;
        double r1479342 = log(r1479341);
        double r1479343 = r1479342 - r1479335;
        double r1479344 = r1479340 + r1479343;
        double r1479345 = r1479334 + r1479344;
        double r1479346 = r1479333 + r1479345;
        return r1479346;
}

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 0.2

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied associate--l+0.2

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

  4. Applied associate-+l+0.2

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

  6. Applied add-cube-cbrt0.2

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

  7. Applied log-prod0.3

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

  8. Applied associate-+l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019129 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))