Average Error: 0.3 → 0.3
Time: 7.0s
Precision: binary64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\log \left(\sqrt{z}\right) + \left(\log \left(\sqrt{z}\right) + \left(\left(a - 0.5\right) \cdot \log t - t\right)\right)\right)\]
\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(\log \left(\sqrt{z}\right) + \left(\log \left(\sqrt{z}\right) + \left(\left(a - 0.5\right) \cdot \log t - t\right)\right)\right)
(FPCore (x y z t a)
 :precision binary64
 (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))
↓
(FPCore (x y z t a)
 :precision binary64
 (+
  (log (+ x y))
  (+ (log (sqrt z)) (+ (log (sqrt z)) (- (* (- a 0.5) (log t)) t)))))
double code(double x, double y, double z, double t, double a) {
	return ((log(x + y) + log(z)) - t) + ((a - 0.5) * log(t));
}
↓
double code(double x, double y, double z, double t, double a) {
	return log(x + y) + (log(sqrt(z)) + (log(sqrt(z)) + (((a - 0.5) * log(t)) - 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

Original0.3
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+_binary64_110240.3

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

  4. Applied associate-+l+_binary64_110200.3

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

  5. Simplified0.3

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

  7. Applied add-sqr-sqrt_binary64_111090.3

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

  8. Applied log-prod_binary64_111730.3

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

  9. Applied associate-+l+_binary64_110200.3

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

  10. Simplified0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020280 
(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))))