Average Error: 0.3 → 0.3
Time: 5.9s
Precision: binary64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt{x + y}\right) + \left(\left(\left(a - 0.5\right) \cdot \log t - t\right) + \left(\log \left(\sqrt{x + y}\right) + \log z\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt{x + y}\right) + \left(\left(\left(a - 0.5\right) \cdot \log t - t\right) + \left(\log \left(\sqrt{x + y}\right) + \log z\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 (sqrt (+ x y)))
  (+ (- (* (- a 0.5) (log t)) t) (+ (log (sqrt (+ x y))) (log z)))))
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) log(((double) sqrt(((double) (x + y)))))) + ((double) (((double) (((double) (((double) (a - 0.5)) * ((double) log(t)))) - t)) + ((double) (((double) log(((double) sqrt(((double) (x + y)))))) + ((double) log(z))))))));
}

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. 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 add-sqr-sqrt0.3

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

  5. Applied log-prod0.3

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

  6. Applied associate-+l+0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020198 
(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))))