Average Error: 0.2 → 0.1
Time: 3.3s
Precision: binary64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[6 \cdot \log \left({e}^{\left(\frac{x - 1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}\right)}\right)\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \log \left({e}^{\left(\frac{x - 1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}\right)}\right)
double code(double x) {
	return ((double) (((double) (6.0 * ((double) (x - 1.0)))) / ((double) (((double) (x + 1.0)) + ((double) (4.0 * ((double) sqrt(x))))))));
}
↓
double code(double x) {
	return ((double) (6.0 * ((double) log(((double) pow(((double) M_E), ((double) (((double) (x - 1.0)) / ((double) (x + ((double) (1.0 + ((double) (4.0 * ((double) sqrt(x))))))))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.1
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{6 \cdot \frac{x - 1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}}\]
  3. Using strategy rm

  4. Applied add-log-exp0.1

    \[\leadsto 6 \cdot \color{blue}{\log \left(e^{\frac{x - 1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}}\right)}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity0.1

    \[\leadsto 6 \cdot \log \left(e^{\frac{x - 1}{\color{blue}{1 \cdot \left(x + \left(1 + 4 \cdot \sqrt{x}\right)\right)}}}\right)\]

  7. Applied *-un-lft-identity0.1

    \[\leadsto 6 \cdot \log \left(e^{\frac{\color{blue}{1 \cdot \left(x - 1\right)}}{1 \cdot \left(x + \left(1 + 4 \cdot \sqrt{x}\right)\right)}}\right)\]

  8. Applied times-frac0.1

    \[\leadsto 6 \cdot \log \left(e^{\color{blue}{\frac{1}{1} \cdot \frac{x - 1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}}}\right)\]

  9. Applied exp-prod0.1

    \[\leadsto 6 \cdot \log \color{blue}{\left({\left(e^{\frac{1}{1}}\right)}^{\left(\frac{x - 1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}\right)}\right)}\]

  10. Simplified0.1

    \[\leadsto 6 \cdot \log \left({\color{blue}{e}}^{\left(\frac{x - 1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}\right)}\right)\]

  11. Final simplification0.1

    \[\leadsto 6 \cdot \log \left({e}^{\left(\frac{x - 1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}\right)}\right)\]

Reproduce

herbie shell --seed 2020184 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"
  :precision binary64

  :herbie-target
  (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

  (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))