Average Error: 0.3 → 0.3
Time: 10.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \frac{\log t}{\frac{1}{a - 0.5}}\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \frac{\log t}{\frac{1}{a - 0.5}}
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(z)) - t) + (log(t) / (1.0 / (a - 0.5))));
}

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 flip--16.1

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

  4. Applied associate-*l/16.3

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

  6. Applied *-commutative16.3

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

  7. Applied associate-/l*16.1

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

  8. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \frac{\log t}{\color{blue}{\frac{1}{a - 0.5}}}\]

  9. Final simplification0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \frac{\log t}{\frac{1}{a - 0.5}}\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(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))))