Average Error: 0.3 → 0.2
Time: 18.8s
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 r401544 = x;
        double r401545 = y;
        double r401546 = r401544 + r401545;
        double r401547 = log(r401546);
        double r401548 = z;
        double r401549 = log(r401548);
        double r401550 = r401547 + r401549;
        double r401551 = t;
        double r401552 = r401550 - r401551;
        double r401553 = a;
        double r401554 = 0.5;
        double r401555 = r401553 - r401554;
        double r401556 = log(r401551);
        double r401557 = r401555 * r401556;
        double r401558 = r401552 + r401557;
        return r401558;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r401559 = x;
        double r401560 = y;
        double r401561 = r401559 + r401560;
        double r401562 = log(r401561);
        double r401563 = z;
        double r401564 = log(r401563);
        double r401565 = t;
        double r401566 = r401564 - r401565;
        double r401567 = a;
        double r401568 = 0.5;
        double r401569 = r401567 - r401568;
        double r401570 = log(r401565);
        double r401571 = r401569 * r401570;
        double r401572 = r401566 + r401571;
        double r401573 = r401562 + r401572;
        return r401573;
}

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
Target0.2
Herbie0.2
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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+0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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))))