Average Error: 14.7 → 14.6
Time: 1.9s
Precision: binary64
\[\frac{\frac{\frac{\left(a + b\right) + c}{a} \cdot \left(\left(a + b\right) - c\right) - 2 \cdot b}{b}}{2}\]
↓
\[\frac{\frac{\left(a + b\right) + c}{a} \cdot \left(\left(a + b\right) - c\right)}{2 \cdot b} + -1\]
\frac{\frac{\frac{\left(a + b\right) + c}{a} \cdot \left(\left(a + b\right) - c\right) - 2 \cdot b}{b}}{2}
↓
\frac{\frac{\left(a + b\right) + c}{a} \cdot \left(\left(a + b\right) - c\right)}{2 \cdot b} + -1
double code(double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (a + b)) + c)) / a)) * ((double) (((double) (a + b)) - c)))) - ((double) (2.0 * b)))) / b)) / 2.0));
}
↓
double code(double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (a + b)) + c)) / a)) * ((double) (((double) (a + b)) - c)))) / ((double) (2.0 * b)))) + -1.0));
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

    \[\frac{\frac{\frac{\left(a + b\right) + c}{a} \cdot \left(\left(a + b\right) - c\right) - 2 \cdot b}{b}}{2}\]

  2. Simplified14.6

    \[\leadsto \color{blue}{\frac{\frac{\left(a + b\right) + c}{a} \cdot \left(\left(a + b\right) - c\right)}{2 \cdot b} + -1}\]

  3. Final simplification14.6

    \[\leadsto \frac{\frac{\left(a + b\right) + c}{a} \cdot \left(\left(a + b\right) - c\right)}{2 \cdot b} + -1\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a b c)
  :name "(/ (/ (- (* (/ (+ (+ a b) c) a) (- (+ a b) c)) (* 2 b)) b) 2)"
  :precision binary64
  (/ (/ (- (* (/ (+ (+ a b) c) a) (- (+ a b) c)) (* 2.0 b)) b) 2.0))