Average Error: 44.0 → 12.0
Time: 14.1s
Precision: 64
\[1.1102230246251565 \cdot 10^{-16} \lt a \lt 9007199254740992.0 \land 1.1102230246251565 \cdot 10^{-16} \lt b \lt 9007199254740992.0 \land 1.1102230246251565 \cdot 10^{-16} \lt c \lt 9007199254740992.0\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{\frac{c}{b} \cdot -2}{2}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\frac{\frac{c}{b} \cdot -2}{2}
double f(double a, double b, double c) {
        double r742202 = b;
        double r742203 = -r742202;
        double r742204 = r742202 * r742202;
        double r742205 = 4.0;
        double r742206 = a;
        double r742207 = r742205 * r742206;
        double r742208 = c;
        double r742209 = r742207 * r742208;
        double r742210 = r742204 - r742209;
        double r742211 = sqrt(r742210);
        double r742212 = r742203 + r742211;
        double r742213 = 2.0;
        double r742214 = r742213 * r742206;
        double r742215 = r742212 / r742214;
        return r742215;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r742216 = c;
        double r742217 = b;
        double r742218 = r742216 / r742217;
        double r742219 = -2.0;
        double r742220 = r742218 * r742219;
        double r742221 = 2.0;
        double r742222 = r742220 / r742221;
        return r742222;
}

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 44.0

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

  2. Simplified44.0

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

  3. Taylor expanded around inf 12.0

    \[\leadsto \frac{\color{blue}{-2 \cdot \frac{c}{b}}}{2}\]

  4. Final simplification12.0

    \[\leadsto \frac{\frac{c}{b} \cdot -2}{2}\]

Reproduce

herbie shell --seed 2019153 
(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 a) c)))) (* 2 a)))