Average Error: 44.2 → 0.4
Time: 17.6s
Precision: 64
\[1.11022 \cdot 10^{-16} \lt a \lt 9.0072 \cdot 10^{15} \land 1.11022 \cdot 10^{-16} \lt b \lt 9.0072 \cdot 10^{15} \land 1.11022 \cdot 10^{-16} \lt c \lt 9.0072 \cdot 10^{15}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{\left(4 \cdot a\right) \cdot c}{\left(-\left(a \cdot b + a \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)\right) \cdot 2}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\frac{\left(4 \cdot a\right) \cdot c}{\left(-\left(a \cdot b + a \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)\right) \cdot 2}
double f(double a, double b, double c) {
        double r48272 = b;
        double r48273 = -r48272;
        double r48274 = r48272 * r48272;
        double r48275 = 4.0;
        double r48276 = a;
        double r48277 = r48275 * r48276;
        double r48278 = c;
        double r48279 = r48277 * r48278;
        double r48280 = r48274 - r48279;
        double r48281 = sqrt(r48280);
        double r48282 = r48273 + r48281;
        double r48283 = 2.0;
        double r48284 = r48283 * r48276;
        double r48285 = r48282 / r48284;
        return r48285;
}
↓
double f(double a, double b, double c) {
        double r48286 = 4.0;
        double r48287 = a;
        double r48288 = r48286 * r48287;
        double r48289 = c;
        double r48290 = r48288 * r48289;
        double r48291 = b;
        double r48292 = r48287 * r48291;
        double r48293 = r48291 * r48291;
        double r48294 = r48293 - r48290;
        double r48295 = sqrt(r48294);
        double r48296 = r48287 * r48295;
        double r48297 = r48292 + r48296;
        double r48298 = -r48297;
        double r48299 = 2.0;
        double r48300 = r48298 * r48299;
        double r48301 = r48290 / r48300;
        return r48301;
}

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 44.2

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

  3. Applied flip-+44.2

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

  4. Simplified0.4

    \[\leadsto \frac{\frac{\color{blue}{0 + \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
  5. Using strategy rm

  6. Applied div-inv0.5

    \[\leadsto \frac{\color{blue}{\left(0 + \left(4 \cdot a\right) \cdot c\right) \cdot \frac{1}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}{2 \cdot a}\]

  7. Applied associate-/l*0.5

    \[\leadsto \color{blue}{\frac{0 + \left(4 \cdot a\right) \cdot c}{\frac{2 \cdot a}{\frac{1}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}}\]

  8. Simplified0.4

    \[\leadsto \frac{0 + \left(4 \cdot a\right) \cdot c}{\color{blue}{\left(a \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)\right) \cdot 2}}\]
  9. Using strategy rm

  10. Applied sub-neg0.4

    \[\leadsto \frac{0 + \left(4 \cdot a\right) \cdot c}{\left(a \cdot \color{blue}{\left(\left(-b\right) + \left(-\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)\right)}\right) \cdot 2}\]

  11. Applied distribute-lft-in0.4

    \[\leadsto \frac{0 + \left(4 \cdot a\right) \cdot c}{\color{blue}{\left(a \cdot \left(-b\right) + a \cdot \left(-\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}\right)\right)} \cdot 2}\]

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019195 
(FPCore (a b c)
  :name "Quadratic roots, medium range"
  :pre (and (< 1.1102230246251565e-16 a 9007199254740992.0) (< 1.1102230246251565e-16 b 9007199254740992.0) (< 1.1102230246251565e-16 c 9007199254740992.0))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))