Average Error: 0.3 → 0.3
Time: 20.0s
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 r137551 = x;
        double r137552 = y;
        double r137553 = r137551 + r137552;
        double r137554 = log(r137553);
        double r137555 = z;
        double r137556 = log(r137555);
        double r137557 = r137554 + r137556;
        double r137558 = t;
        double r137559 = r137557 - r137558;
        double r137560 = a;
        double r137561 = 0.5;
        double r137562 = r137560 - r137561;
        double r137563 = log(r137558);
        double r137564 = r137562 * r137563;
        double r137565 = r137559 + r137564;
        return r137565;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r137566 = x;
        double r137567 = y;
        double r137568 = r137566 + r137567;
        double r137569 = log(r137568);
        double r137570 = z;
        double r137571 = log(r137570);
        double r137572 = t;
        double r137573 = r137571 - r137572;
        double r137574 = a;
        double r137575 = 0.5;
        double r137576 = r137574 - r137575;
        double r137577 = log(r137572);
        double r137578 = r137576 * r137577;
        double r137579 = r137573 + r137578;
        double r137580 = r137569 + r137579;
        return r137580;
}

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 2020045 
(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))))