Average Error: 26.3 → 26.3
Time: 1.4s
Precision: binary64
\[\sqrt{4 \cdot \left(a \cdot c\right) + {b}^{2}}\]
↓
\[\sqrt{4 \cdot \left(a \cdot c\right) + {b}^{2}}\]
\sqrt{4 \cdot \left(a \cdot c\right) + {b}^{2}}
↓
\sqrt{4 \cdot \left(a \cdot c\right) + {b}^{2}}
double code(double a, double c, double b) {
	return ((double) sqrt(((double) (((double) (4.0 * ((double) (a * c)))) + ((double) pow(b, 2.0))))));
}
↓
double code(double a, double c, double b) {
	return ((double) sqrt(((double) (((double) (4.0 * ((double) (a * c)))) + ((double) pow(b, 2.0))))));
}

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 26.3

    \[\sqrt{4 \cdot \left(a \cdot c\right) + {b}^{2}}\]

  2. Final simplification26.3

    \[\leadsto \sqrt{4 \cdot \left(a \cdot c\right) + {b}^{2}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (a c b)
  :name "(sqrt (+ (* 4 (* a c)) (pow b 2)))"
  :precision binary64
  (sqrt (+ (* 4.0 (* a c)) (pow b 2.0))))