Average Error: 34.0 → 34.0
Time: 2.2s
Precision: binary64
\[\frac{\sqrt{4 \cdot \left(a \cdot c\right) + {b}^{2}} - b}{2 \cdot a}\]
↓
\[\frac{\sqrt{4 \cdot \left(a \cdot c\right) + {b}^{2}} - b}{2 \cdot a}\]
\frac{\sqrt{4 \cdot \left(a \cdot c\right) + {b}^{2}} - b}{2 \cdot a}
↓
\frac{\sqrt{4 \cdot \left(a \cdot c\right) + {b}^{2}} - b}{2 \cdot a}
double code(double a, double c, double b) {
	return ((double) (((double) (((double) sqrt(((double) (((double) (4.0 * ((double) (a * c)))) + ((double) pow(b, 2.0)))))) - b)) / ((double) (2.0 * a))));
}
↓
double code(double a, double c, double b) {
	return ((double) (((double) (((double) sqrt(((double) (((double) (4.0 * ((double) (a * c)))) + ((double) pow(b, 2.0)))))) - b)) / ((double) (2.0 * a))));
}

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 34.0

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

  2. Final simplification34.0

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

Reproduce

herbie shell --seed 2020153 
(FPCore (a c b)
  :name "(/ (- (sqrt (+ (* 4 (* a c)) (pow b 2))) b) (* 2 a))"
  :precision binary64
  (/ (- (sqrt (+ (* 4.0 (* a c)) (pow b 2.0))) b) (* 2.0 a)))