Average Error: 52.6 → 0.4
Time: 10.5s
Precision: 64
\[4.93038 \cdot 10^{-32} \lt a \lt 2.02824 \cdot 10^{31} \land 4.93038 \cdot 10^{-32} \lt b \lt 2.02824 \cdot 10^{31} \land 4.93038 \cdot 10^{-32} \lt c \lt 2.02824 \cdot 10^{31}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{\left({b}^{2} - {b}^{2}\right) + 4 \cdot \left(a \cdot c\right)}{a} \cdot \frac{\frac{1}{\left(-b\right) - \sqrt{{\left(b \cdot b - \left(4 \cdot a\right) \cdot c\right)}^{1}}}}{2}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\frac{\left({b}^{2} - {b}^{2}\right) + 4 \cdot \left(a \cdot c\right)}{a} \cdot \frac{\frac{1}{\left(-b\right) - \sqrt{{\left(b \cdot b - \left(4 \cdot a\right) \cdot c\right)}^{1}}}}{2}
double code(double a, double b, double c) {
	return ((double) (((double) (((double) -(b)) + ((double) sqrt(((double) (((double) (b * b)) - ((double) (((double) (4.0 * a)) * c)))))))) / ((double) (2.0 * a))));
}
↓
double code(double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (((double) pow(b, 2.0)) - ((double) pow(b, 2.0)))) + ((double) (4.0 * ((double) (a * c)))))) / a)) * ((double) (((double) (1.0 / ((double) (((double) -(b)) - ((double) sqrt(((double) pow(((double) (((double) (b * b)) - ((double) (((double) (4.0 * a)) * c)))), 1.0)))))))) / 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 52.6

    \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
  2. Using strategy rm

  3. Applied flip-+52.6

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

  4. Simplified0.4

    \[\leadsto \frac{\frac{\color{blue}{\left({b}^{2} - {b}^{2}\right) + 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
  5. Using strategy rm

  6. Applied pow10.4

    \[\leadsto \frac{\frac{\left({b}^{2} - {b}^{2}\right) + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{\color{blue}{{\left(b \cdot b - \left(4 \cdot a\right) \cdot c\right)}^{1}}}}}{2 \cdot a}\]
  7. Using strategy rm

  8. Applied *-commutative0.4

    \[\leadsto \frac{\frac{\left({b}^{2} - {b}^{2}\right) + 4 \cdot \left(a \cdot c\right)}{\left(-b\right) - \sqrt{{\left(b \cdot b - \left(4 \cdot a\right) \cdot c\right)}^{1}}}}{\color{blue}{a \cdot 2}}\]

  9. Applied div-inv0.5

    \[\leadsto \frac{\color{blue}{\left(\left({b}^{2} - {b}^{2}\right) + 4 \cdot \left(a \cdot c\right)\right) \cdot \frac{1}{\left(-b\right) - \sqrt{{\left(b \cdot b - \left(4 \cdot a\right) \cdot c\right)}^{1}}}}}{a \cdot 2}\]

  10. Applied times-frac0.4

    \[\leadsto \color{blue}{\frac{\left({b}^{2} - {b}^{2}\right) + 4 \cdot \left(a \cdot c\right)}{a} \cdot \frac{\frac{1}{\left(-b\right) - \sqrt{{\left(b \cdot b - \left(4 \cdot a\right) \cdot c\right)}^{1}}}}{2}}\]

  11. Final simplification0.4

    \[\leadsto \frac{\left({b}^{2} - {b}^{2}\right) + 4 \cdot \left(a \cdot c\right)}{a} \cdot \frac{\frac{1}{\left(-b\right) - \sqrt{{\left(b \cdot b - \left(4 \cdot a\right) \cdot c\right)}^{1}}}}{2}\]

Reproduce

herbie shell --seed 2020114 
(FPCore (a b c)
  :name "Quadratic roots, wide range"
  :precision binary64
  :pre (and (< 4.9303800000000003e-32 a 2.02824e+31) (< 4.9303800000000003e-32 b 2.02824e+31) (< 4.9303800000000003e-32 c 2.02824e+31))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))