Average Error: 8.3 → 8.3
Time: 1.0s
Precision: binary64
\[\frac{p \cdot q}{1 - \left(p \cdot \left(1 - q\right) + \left(1 - p\right) \cdot q\right)}\]
↓
\[\frac{p \cdot q}{1 - \left(p \cdot \left(1 - q\right) + \left(1 - p\right) \cdot q\right)}\]
\frac{p \cdot q}{1 - \left(p \cdot \left(1 - q\right) + \left(1 - p\right) \cdot q\right)}
↓
\frac{p \cdot q}{1 - \left(p \cdot \left(1 - q\right) + \left(1 - p\right) \cdot q\right)}
double code(double p, double q) {
	return ((double) (((double) (p * q)) / ((double) (1.0 - ((double) (((double) (p * ((double) (1.0 - q)))) + ((double) (((double) (1.0 - p)) * q))))))));
}
↓
double code(double p, double q) {
	return ((double) (((double) (p * q)) / ((double) (1.0 - ((double) (((double) (p * ((double) (1.0 - q)))) + ((double) (((double) (1.0 - p)) * q))))))));
}

Error

Bits error versus p

Bits error versus q

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 8.3

    \[\frac{p \cdot q}{1 - \left(p \cdot \left(1 - q\right) + \left(1 - p\right) \cdot q\right)}\]

  2. Final simplification8.3

    \[\leadsto \frac{p \cdot q}{1 - \left(p \cdot \left(1 - q\right) + \left(1 - p\right) \cdot q\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (p q)
  :name "(/ (* p q) (- 1.0 (+ (* p (- 1.0 q)) (* (- 1.0 p) q))))"
  :precision binary64
  (/ (* p q) (- 1.0 (+ (* p (- 1.0 q)) (* (- 1.0 p) q)))))