Average Error: 0.5 → 0.5
Time: 1.7s
Precision: binary64
\[a + \log \left(1 + e^{b - a}\right)\]
↓
\[a + \log \left(1 + e^{b - a}\right)\]
a + \log \left(1 + e^{b - a}\right)
↓
a + \log \left(1 + e^{b - a}\right)
double code(double a, double b) {
	return ((double) (a + ((double) log(((double) (1.0 + ((double) exp(((double) (b - a))))))))));
}
↓
double code(double a, double b) {
	return ((double) (a + ((double) log(((double) (1.0 + ((double) exp(((double) (b - a))))))))));
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[a + \log \left(1 + e^{b - a}\right)\]

  2. Final simplification0.5

    \[\leadsto a + \log \left(1 + e^{b - a}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a b)
  :name "(+ a (log (+ 1 (exp (- b a)))))"
  :precision binary64
  (+ a (log (+ 1.0 (exp (- b a))))))