Average Error: 3.8 → 3.8
Time: 1.4s
Precision: binary64
\[\frac{w \cdot \left(1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}\right)}{2}\]
↓
\[\frac{w \cdot \left(1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}\right)}{2}\]
\frac{w \cdot \left(1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}\right)}{2}
↓
\frac{w \cdot \left(1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}\right)}{2}
double code(double w, double d, double a) {
	return ((double) (((double) (w * ((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) (((double) (4.0 * d)) * a)))))))))) / 2.0));
}
↓
double code(double w, double d, double a) {
	return ((double) (((double) (w * ((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) (((double) (4.0 * d)) * a)))))))))) / 2.0));
}

Error

Bits error versus w

Bits error versus d

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.8

    \[\frac{w \cdot \left(1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}\right)}{2}\]

  2. Final simplification3.8

    \[\leadsto \frac{w \cdot \left(1 + \sqrt{1 - \left(4 \cdot d\right) \cdot a}\right)}{2}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (w d a)
  :name "(/ (* w (+ 1.0 (sqrt (- 1.0 (* (* 4.0 d) a))))) 2.0)"
  :precision binary64
  (/ (* w (+ 1.0 (sqrt (- 1.0 (* (* 4.0 d) a))))) 2.0))