Average Error: 0.3 → 0.3
Time: 12.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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]{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
double f(double x, double y, double z, double t, double a) {
        double r70328 = x;
        double r70329 = y;
        double r70330 = r70328 + r70329;
        double r70331 = log(r70330);
        double r70332 = z;
        double r70333 = log(r70332);
        double r70334 = r70331 + r70333;
        double r70335 = t;
        double r70336 = r70334 - r70335;
        double r70337 = a;
        double r70338 = 0.5;
        double r70339 = r70337 - r70338;
        double r70340 = log(r70335);
        double r70341 = r70339 * r70340;
        double r70342 = r70336 + r70341;
        return r70342;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r70343 = x;
        double r70344 = y;
        double r70345 = r70343 + r70344;
        double r70346 = cbrt(r70345);
        double r70347 = r70346 * r70346;
        double r70348 = log(r70347);
        double r70349 = log(r70346);
        double r70350 = z;
        double r70351 = log(r70350);
        double r70352 = r70349 + r70351;
        double r70353 = r70348 + r70352;
        double r70354 = t;
        double r70355 = r70353 - r70354;
        double r70356 = a;
        double r70357 = 0.5;
        double r70358 = r70356 - r70357;
        double r70359 = log(r70354);
        double r70360 = r70358 * r70359;
        double r70361 = r70355 + r70360;
        return r70361;
}

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

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

Reproduce

herbie shell --seed 2020018 
(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))))