Average Error: 0.3 → 0.3
Time: 14.5s
Precision: binary64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt{x + y}\right) + \left(\log \left(\sqrt{x + y}\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)\]
\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(\log \left(\sqrt{x + y}\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)
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) log(((double) sqrt(((double) (x + y)))))) + ((double) (((double) (((double) log(z)) - t)) + ((double) (((double) (a - 0.5)) * ((double) log(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

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. Using strategy rm

  6. Applied add-sqr-sqrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied associate-+l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020147 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))