Average Error: 0.3 → 0.3
Time: 11.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r297426 = x;
        double r297427 = y;
        double r297428 = r297426 + r297427;
        double r297429 = log(r297428);
        double r297430 = z;
        double r297431 = log(r297430);
        double r297432 = r297429 + r297431;
        double r297433 = t;
        double r297434 = r297432 - r297433;
        double r297435 = a;
        double r297436 = 0.5;
        double r297437 = r297435 - r297436;
        double r297438 = log(r297433);
        double r297439 = r297437 * r297438;
        double r297440 = r297434 + r297439;
        return r297440;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r297441 = x;
        double r297442 = y;
        double r297443 = r297441 + r297442;
        double r297444 = log(r297443);
        double r297445 = z;
        double r297446 = log(r297445);
        double r297447 = t;
        double r297448 = r297446 - r297447;
        double r297449 = a;
        double r297450 = 0.5;
        double r297451 = r297449 - r297450;
        double r297452 = log(r297447);
        double r297453 = r297451 * r297452;
        double r297454 = r297448 + r297453;
        double r297455 = r297444 + r297454;
        return r297455;
}

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 associate--l+0.3

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

  4. Applied associate-+l+0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020027 
(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))))