Average Error: 0.3 → 0.3
Time: 12.0s
Precision: binary64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log \left(x + y\right) + \log t \cdot a\right) - \left(\log t \cdot 0.5 + \left(t - \log z\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log \left(x + y\right) + \log t \cdot a\right) - \left(\log t \cdot 0.5 + \left(t - \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 (+ x y)) (* (log t) a)) (+ (* (log t) 0.5) (- t (log z)))))
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(t) * a)) - ((log(t) * 0.5) + (t - 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. Using strategy rm

  3. Applied add-cube-cbrt_binary64_89790.3

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

  4. Applied log-prod_binary64_90300.3

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

  5. Applied distribute-rgt-in_binary64_88940.3

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

  6. Applied associate-+r+_binary64_88760.3

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

  7. Simplified0.3

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

  8. Taylor expanded around inf 0.4

    \[\leadsto \color{blue}{\left(\log \left(x + y\right) + 3 \cdot \left(a \cdot \log \left({t}^{0.3333333333333333}\right)\right)\right) - \left(1.5 \cdot \log \left({t}^{0.3333333333333333}\right) + \left(\log \left(\frac{1}{z}\right) + t\right)\right)}\]

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2021043 
(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))))