Average Error: 0.1 → 0.1
Time: 1.0s
Precision: binary64
\[\frac{\lambda}{2 \cdot \sqrt{2^{m} + delta}}\]
↓
\[\frac{\lambda}{2 \cdot \sqrt{2^{m} + delta}}\]
\frac{\lambda}{2 \cdot \sqrt{2^{m} + delta}}
↓
\frac{\lambda}{2 \cdot \sqrt{2^{m} + delta}}
double code(double lambda, double m, double delta) {
	return ((double) (lambda / ((double) (2.0 * ((double) sqrt(((double) (((double) exp2(m)) + delta))))))));
}
↓
double code(double lambda, double m, double delta) {
	return ((double) (lambda / ((double) (2.0 * ((double) sqrt(((double) (((double) exp2(m)) + delta))))))));
}

Error

Bits error versus lambda

Bits error versus m

Bits error versus delta

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{\lambda}{2 \cdot \sqrt{2^{m} + delta}}\]

  2. Final simplification0.1

    \[\leadsto \frac{\lambda}{2 \cdot \sqrt{2^{m} + delta}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (lambda m delta)
  :name "(/ lambda (* 2 (sqrt (+ (exp2 m) delta))))"
  :precision binary64
  (/ lambda (* 2.0 (sqrt (+ (exp2 m) delta)))))