Average Error: 8.2 → 0.1
Time: 867.0ms
Precision: binary64
\[\frac{a \cdot b}{\left(1 - b\right) + a \cdot b}\]
↓
\[\frac{a}{\frac{1 - b}{b} + a}\]
\frac{a \cdot b}{\left(1 - b\right) + a \cdot b}
↓
\frac{a}{\frac{1 - b}{b} + a}
double code(double a, double b) {
	return ((double) (((double) (a * b)) / ((double) (((double) (1.0 - b)) + ((double) (a * b))))));
}
↓
double code(double a, double b) {
	return ((double) (a / ((double) (((double) (((double) (1.0 - b)) / 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 8.2

    \[\frac{a \cdot b}{\left(1 - b\right) + a \cdot b}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{a}{\frac{1 - b}{b} + a}}\]

  3. Final simplification0.1

    \[\leadsto \frac{a}{\frac{1 - b}{b} + a}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a b)
  :name "(/ (* a b) (+ (- 1.0 b) (* a b)))"
  :precision binary64
  (/ (* a b) (+ (- 1.0 b) (* a b))))