Average Error: 0.3 → 0.3
Time: 13.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log z + \left(\left(\log \left(x + y\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log z + \left(\left(\log \left(x + y\right) - t\right) + \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({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)\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(z)) + ((double) (((double) (((double) log(((double) (x + y)))) - t)) + ((double) (((double) (((double) (a - 0.5)) * ((double) (2.0 * ((double) log(((double) cbrt(t)))))))) + ((double) (((double) (a - 0.5)) * ((double) log(((double) pow(((double) (1.0 / t)), -0.3333333333333333))))))))))));
}

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 +-commutative0.3

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

  4. Applied associate--l+0.3

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

  5. Applied associate-+l+0.3

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

  7. Applied add-cube-cbrt0.3

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

  8. Applied log-prod0.3

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

  9. Applied distribute-lft-in0.3

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

  10. Simplified0.3

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

  11. Taylor expanded around inf 0.3

    \[\leadsto \log z + \left(\left(\log \left(x + y\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)}\right)\right)\]

  12. Final simplification0.3

    \[\leadsto \log z + \left(\left(\log \left(x + y\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020113 
(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))))