Average Error: 39.5 → 0.6
Time: 3.3s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) log(((double) (1.0 + x))));
}

↓
double code(double x) {
	double VAR;
	if ((((double) (1.0 + x)) <= 1.0)) {
		VAR = ((double) (((double) log(1.0)) + ((double) (x * ((double) (1.0 - ((double) (((double) (x * 0.5)) / ((double) (1.0 * 1.0))))))))));
	} else {
		VAR = ((double) (((double) log(((double) sqrt(((double) (1.0 + x)))))) + ((double) log(((double) sqrt(((double) (1.0 + x))))))));
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original39.5
Target0.2
Herbie0.6
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  (+ 1.0 x)  < 1
    1. Initial program 59.6
      \[\]
    2. Taylor expanded around 0 0.3
      \[\leadsto \]
    3. Simplified0.3
      \[\leadsto \]
    if 1 <  (+ 1.0 x) 
    1. Initial program 1.1
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt1.2
      \[\leadsto \]
    4. Applied log-prod1.2
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.6
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (x)
  :name "ln(1 + x)"
  :precision binary64

  :herbie-target
  (if (== (+ 1.0 x) 1.0) x (/ (* x (log (+ 1.0 x))) (- (+ 1.0 x) 1.0)))

  (log (+ 1.0 x)))