Average Error: 2.4 → 2.4
Time: 3.9s
Precision: binary64
\[\log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)\]
↓
\[\log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)\]
\log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)
↓
\log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)
double code(double e, double x) {
	return ((double) log(((double) (((double) (1.0 / 2.0)) * ((double) (((double) sqrt(((double) (((double) (4.0 * ((double) pow(e, x)))) + 1.0)))) - 1.0))))));
}
↓
double code(double e, double x) {
	return ((double) log(((double) (((double) (1.0 / 2.0)) * ((double) (((double) sqrt(((double) (((double) (4.0 * ((double) pow(e, x)))) + 1.0)))) - 1.0))))));
}

Error

Bits error versus e

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.4

    \[\log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)\]

  2. Final simplification2.4

    \[\leadsto \log \left(\frac{1}{2} \cdot \left(\sqrt{4 \cdot {e}^{x} + 1} - 1\right)\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (e x)
  :name "(log (* (/ 1.0 2.0) (- (sqrt (+ (* 4.0 (pow e x)) 1.0)) 1.0)))"
  :precision binary64
  (log (* (/ 1.0 2.0) (- (sqrt (+ (* 4.0 (pow e x)) 1.0)) 1.0))))