Average Error: 0.3 → 0.3
Time: 29.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log t + 3 \cdot \log \left(\sqrt[3]{x + y}\right)\right) + \left(\log z - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(a - 0.5\right) \cdot \log t + 3 \cdot \log \left(\sqrt[3]{x + y}\right)\right) + \left(\log z - t\right)
double f(double x, double y, double z, double t, double a) {
        double r55471 = x;
        double r55472 = y;
        double r55473 = r55471 + r55472;
        double r55474 = log(r55473);
        double r55475 = z;
        double r55476 = log(r55475);
        double r55477 = r55474 + r55476;
        double r55478 = t;
        double r55479 = r55477 - r55478;
        double r55480 = a;
        double r55481 = 0.5;
        double r55482 = r55480 - r55481;
        double r55483 = log(r55478);
        double r55484 = r55482 * r55483;
        double r55485 = r55479 + r55484;
        return r55485;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r55486 = a;
        double r55487 = 0.5;
        double r55488 = r55486 - r55487;
        double r55489 = t;
        double r55490 = log(r55489);
        double r55491 = r55488 * r55490;
        double r55492 = 3.0;
        double r55493 = x;
        double r55494 = y;
        double r55495 = r55493 + r55494;
        double r55496 = cbrt(r55495);
        double r55497 = log(r55496);
        double r55498 = r55492 * r55497;
        double r55499 = r55491 + r55498;
        double r55500 = z;
        double r55501 = log(r55500);
        double r55502 = r55501 - r55489;
        double r55503 = r55499 + r55502;
        return r55503;
}

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

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

Reproduce

herbie shell --seed 2019291 
(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))))