Average Error: 0.3 → 0.3
Time: 15.5s
Precision: binary64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(\log z - \left(t - \log \left(x + y\right)\right)\right)\]
\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 \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(\log z - \left(t - \log \left(x + y\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
 (+
  (+ (* (- a 0.5) (* 2.0 (log (cbrt t)))) (* (- a 0.5) (log (cbrt t))))
  (- (log z) (- t (log (+ x y))))))
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 (((a - 0.5) * (2.0 * log(cbrt(t)))) + ((a - 0.5) * log(cbrt(t)))) + (log(z) - (t - log(x + y)));
}

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

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

  4. Applied add-cube-cbrt_binary64_171630.3

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

  5. Applied log-prod_binary64_172140.3

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

  6. Applied distribute-rgt-in_binary64_170780.3

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

  7. Simplified0.3

    \[\leadsto \left(\color{blue}{\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right)} + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) - \left(\left(t - \log \left(x + y\right)\right) - \log z\right)\]

  8. Final simplification0.3

    \[\leadsto \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(\log z - \left(t - \log \left(x + y\right)\right)\right)\]

Reproduce

herbie shell --seed 2021176 
(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))))