Average Error: 0.3 → 0.3
Time: 11.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left({\left(x + y\right)}^{\frac{1}{3}}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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({\left(x + y\right)}^{\frac{1}{3}}\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 r343344 = x;
        double r343345 = y;
        double r343346 = r343344 + r343345;
        double r343347 = log(r343346);
        double r343348 = z;
        double r343349 = log(r343348);
        double r343350 = r343347 + r343349;
        double r343351 = t;
        double r343352 = r343350 - r343351;
        double r343353 = a;
        double r343354 = 0.5;
        double r343355 = r343353 - r343354;
        double r343356 = log(r343351);
        double r343357 = r343355 * r343356;
        double r343358 = r343352 + r343357;
        return r343358;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r343359 = x;
        double r343360 = y;
        double r343361 = r343359 + r343360;
        double r343362 = cbrt(r343361);
        double r343363 = r343362 * r343362;
        double r343364 = log(r343363);
        double r343365 = 0.3333333333333333;
        double r343366 = pow(r343361, r343365);
        double r343367 = log(r343366);
        double r343368 = z;
        double r343369 = log(r343368);
        double r343370 = r343367 + r343369;
        double r343371 = r343364 + r343370;
        double r343372 = t;
        double r343373 = r343371 - r343372;
        double r343374 = a;
        double r343375 = 0.5;
        double r343376 = r343374 - r343375;
        double r343377 = log(r343372);
        double r343378 = r343376 * r343377;
        double r343379 = r343373 + r343378;
        return r343379;
}

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 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. Using strategy rm

  7. Applied pow1/30.3

    \[\leadsto \left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \color{blue}{\left({\left(x + y\right)}^{\frac{1}{3}}\right)} + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  8. Final simplification0.3

    \[\leadsto \left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left({\left(x + y\right)}^{\frac{1}{3}}\right) + \log z\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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