Average Error: 30.7 → 0
Time: 1.1s
Precision: binary64
\[\left(a \cdot 10^{11} + \frac{b}{10^{11}}\right) - a \cdot 10^{11}\]
↓
\[\frac{b}{10^{11}}\]
\left(a \cdot 10^{11} + \frac{b}{10^{11}}\right) - a \cdot 10^{11}
↓
\frac{b}{10^{11}}
double code(double a, double b) {
	return ((double) (((double) (((double) (a * 100000000000.0)) + ((double) (b / 100000000000.0)))) - ((double) (a * 100000000000.0))));
}
↓
double code(double a, double b) {
	return ((double) (b / 100000000000.0));
}

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 30.7

    \[\left(a \cdot 10^{11} + \frac{b}{10^{11}}\right) - a \cdot 10^{11}\]

  2. Simplified0

    \[\leadsto \color{blue}{\frac{b}{10^{11}}}\]

  3. Final simplification0

    \[\leadsto \frac{b}{10^{11}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a b)
  :name "(- (+ (* a 100000000000) (/ b 100000000000)) (* a 100000000000))"
  :precision binary64
  (- (+ (* a 100000000000.0) (/ b 100000000000.0)) (* a 100000000000.0)))