Average Error: 0.3 → 0.3
Time: 23.9s
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 r54523 = x;
        double r54524 = y;
        double r54525 = r54523 + r54524;
        double r54526 = log(r54525);
        double r54527 = z;
        double r54528 = log(r54527);
        double r54529 = r54526 + r54528;
        double r54530 = t;
        double r54531 = r54529 - r54530;
        double r54532 = a;
        double r54533 = 0.5;
        double r54534 = r54532 - r54533;
        double r54535 = log(r54530);
        double r54536 = r54534 * r54535;
        double r54537 = r54531 + r54536;
        return r54537;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r54538 = a;
        double r54539 = 0.5;
        double r54540 = r54538 - r54539;
        double r54541 = t;
        double r54542 = log(r54541);
        double r54543 = r54540 * r54542;
        double r54544 = 3.0;
        double r54545 = x;
        double r54546 = y;
        double r54547 = r54545 + r54546;
        double r54548 = cbrt(r54547);
        double r54549 = log(r54548);
        double r54550 = r54544 * r54549;
        double r54551 = r54543 + r54550;
        double r54552 = z;
        double r54553 = log(r54552);
        double r54554 = r54553 - r54541;
        double r54555 = r54551 + r54554;
        return r54555;
}

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 2019308 
(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))))