Average Error: 33.2 → 33.2
Time: 1.6s
Precision: binary64
\[\frac{\frac{\frac{\left(a \cdot a + b \cdot b\right) - c \cdot c}{a}}{b}}{2}\]
↓
\[\frac{\frac{\frac{\left(a \cdot a + b \cdot b\right) - c \cdot c}{a}}{b}}{2}\]
\frac{\frac{\frac{\left(a \cdot a + b \cdot b\right) - c \cdot c}{a}}{b}}{2}
↓
\frac{\frac{\frac{\left(a \cdot a + b \cdot b\right) - c \cdot c}{a}}{b}}{2}
double code(double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (a * a)) + ((double) (b * b)))) - ((double) (c * c)))) / a)) / b)) / 2.0));
}
↓
double code(double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (a * a)) + ((double) (b * b)))) - ((double) (c * c)))) / a)) / b)) / 2.0));
}

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 33.2

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

  2. Final simplification33.2

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

Reproduce

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