Average Error: 0.3 → 0.3
Time: 16.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{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 r56497 = x;
        double r56498 = y;
        double r56499 = r56497 + r56498;
        double r56500 = log(r56499);
        double r56501 = z;
        double r56502 = log(r56501);
        double r56503 = r56500 + r56502;
        double r56504 = t;
        double r56505 = r56503 - r56504;
        double r56506 = a;
        double r56507 = 0.5;
        double r56508 = r56506 - r56507;
        double r56509 = log(r56504);
        double r56510 = r56508 * r56509;
        double r56511 = r56505 + r56510;
        return r56511;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r56512 = x;
        double r56513 = y;
        double r56514 = r56512 + r56513;
        double r56515 = log(r56514);
        double r56516 = z;
        double r56517 = sqrt(r56516);
        double r56518 = log(r56517);
        double r56519 = r56515 + r56518;
        double r56520 = r56519 + r56518;
        double r56521 = t;
        double r56522 = r56520 - r56521;
        double r56523 = a;
        double r56524 = 0.5;
        double r56525 = r56523 - r56524;
        double r56526 = log(r56521);
        double r56527 = r56525 * r56526;
        double r56528 = r56522 + r56527;
        return r56528;
}

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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 
(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))))