Average Error: 37.7 → 37.7
Time: 1.5s
Precision: binary64
\[\sqrt{\left(\left(a \cdot a + \left(2 \cdot a\right) \cdot c\right) + c \cdot c\right) - \left(a \cdot c + b \cdot b\right)}\]
↓
\[\sqrt{\left(\left(a \cdot a + \left(2 \cdot a\right) \cdot c\right) + c \cdot c\right) - \left(a \cdot c + b \cdot b\right)}\]
\sqrt{\left(\left(a \cdot a + \left(2 \cdot a\right) \cdot c\right) + c \cdot c\right) - \left(a \cdot c + b \cdot b\right)}
↓
\sqrt{\left(\left(a \cdot a + \left(2 \cdot a\right) \cdot c\right) + c \cdot c\right) - \left(a \cdot c + b \cdot b\right)}
double code(double a, double c, double b) {
	return ((double) sqrt(((double) (((double) (((double) (((double) (a * a)) + ((double) (((double) (2.0 * a)) * c)))) + ((double) (c * c)))) - ((double) (((double) (a * c)) + ((double) (b * b))))))));
}
↓
double code(double a, double c, double b) {
	return ((double) sqrt(((double) (((double) (((double) (((double) (a * a)) + ((double) (((double) (2.0 * a)) * c)))) + ((double) (c * c)))) - ((double) (((double) (a * c)) + ((double) (b * b))))))));
}

Error

Bits error versus a

Bits error versus c

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 37.7

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

  2. Final simplification37.7

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

Reproduce

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