Average Error: 0.2 → 0.2
Time: 5.6s
Precision: binary64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log t + \left(\log z + \log \left(x + y\right)\right)\right) - t\]
\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 + \left(\log z + \log \left(x + y\right)\right)\right) - t
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (((double) (((double) log(((double) (x + y)))) + ((double) log(z)))) - t)) + ((double) (((double) (a - 0.5)) * ((double) log(t))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (((double) (((double) (((double) (a - 0.5)) * ((double) log(t)))) + ((double) (((double) log(z)) + ((double) log(((double) (x + y)))))))) - t));
}

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

Original0.2
Target0.3
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 0.2

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

  2. Simplified0.3

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

  4. Applied associate-+r-0.3

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

  5. Applied associate-+r-0.2

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020185 
(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))))