Average Error: 0.3 → 0.3
Time: 1.1m
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\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 r5423327 = x;
        double r5423328 = y;
        double r5423329 = r5423327 + r5423328;
        double r5423330 = log(r5423329);
        double r5423331 = z;
        double r5423332 = log(r5423331);
        double r5423333 = r5423330 + r5423332;
        double r5423334 = t;
        double r5423335 = r5423333 - r5423334;
        double r5423336 = a;
        double r5423337 = 0.5;
        double r5423338 = r5423336 - r5423337;
        double r5423339 = log(r5423334);
        double r5423340 = r5423338 * r5423339;
        double r5423341 = r5423335 + r5423340;
        return r5423341;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r5423342 = y;
        double r5423343 = x;
        double r5423344 = r5423342 + r5423343;
        double r5423345 = cbrt(r5423344);
        double r5423346 = r5423345 * r5423345;
        double r5423347 = log(r5423346);
        double r5423348 = z;
        double r5423349 = log(r5423348);
        double r5423350 = log(r5423345);
        double r5423351 = r5423349 + r5423350;
        double r5423352 = r5423347 + r5423351;
        double r5423353 = t;
        double r5423354 = r5423352 - r5423353;
        double r5423355 = a;
        double r5423356 = 0.5;
        double r5423357 = r5423355 - r5423356;
        double r5423358 = log(r5423353);
        double r5423359 = r5423357 * r5423358;
        double r5423360 = r5423354 + r5423359;
        return r5423360;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(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))))