Average Error: 39.5 → 39.5
Time: 5.7s
Precision: binary64
\[\log \left(1 + x\right)\]
↓
\[\log \left(1 + x\right)\]
\log \left(1 + x\right)
↓
\log \left(1 + x\right)
(FPCore (x) :precision binary64 (log (+ 1.0 x)))
↓
(FPCore (x) :precision binary64 (log (+ 1.0 x)))
double code(double x) {
	return log(1.0 + x);
}
↓
double code(double x) {
	return log(1.0 + x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original39.5
Target0.2
Herbie39.5
\[\begin{array}{l} \mathbf{if}\;1 + x = 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \log \left(1 + x\right)}{\left(1 + x\right) - 1}\\ \end{array}\]

Derivation

  1. Initial program 39.5

    \[\log \left(1 + x\right)\]

  2. Final simplification39.5

    \[\leadsto \log \left(1 + x\right)\]

Reproduce

herbie shell --seed 2020268 
(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)))