Average Error: 52.7 → 6.1
Time: 18.4s
Precision: 64
\[4.930380657631324 \cdot 10^{-32} \lt a \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt b \lt 2.028240960365167 \cdot 10^{+31} \land 4.930380657631324 \cdot 10^{-32} \lt c \lt 2.028240960365167 \cdot 10^{+31}\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{-c}{b}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\frac{-c}{b}
double f(double a, double b, double c) {
        double r978235 = b;
        double r978236 = -r978235;
        double r978237 = r978235 * r978235;
        double r978238 = 4.0;
        double r978239 = a;
        double r978240 = r978238 * r978239;
        double r978241 = c;
        double r978242 = r978240 * r978241;
        double r978243 = r978237 - r978242;
        double r978244 = sqrt(r978243);
        double r978245 = r978236 + r978244;
        double r978246 = 2.0;
        double r978247 = r978246 * r978239;
        double r978248 = r978245 / r978247;
        return r978248;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r978249 = c;
        double r978250 = -r978249;
        double r978251 = b;
        double r978252 = r978250 / r978251;
        return r978252;
}

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 52.7

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

  2. Simplified52.7

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

  3. Taylor expanded around inf 6.1

    \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]

  4. Simplified6.1

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

  5. Final simplification6.1

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

Reproduce

herbie shell --seed 2019165 
(FPCore (a b c)
  :name "Quadratic roots, wide range"
  :pre (and (< 4.930380657631324e-32 a 2.028240960365167e+31) (< 4.930380657631324e-32 b 2.028240960365167e+31) (< 4.930380657631324e-32 c 2.028240960365167e+31))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))