Average Error: 52.7 → 6.1
Time: 51.4s
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 r6214928 = b;
        double r6214929 = -r6214928;
        double r6214930 = r6214928 * r6214928;
        double r6214931 = 4.0;
        double r6214932 = a;
        double r6214933 = r6214931 * r6214932;
        double r6214934 = c;
        double r6214935 = r6214933 * r6214934;
        double r6214936 = r6214930 - r6214935;
        double r6214937 = sqrt(r6214936);
        double r6214938 = r6214929 + r6214937;
        double r6214939 = 2.0;
        double r6214940 = r6214939 * r6214932;
        double r6214941 = r6214938 / r6214940;
        return r6214941;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r6214942 = c;
        double r6214943 = b;
        double r6214944 = r6214942 / r6214943;
        double r6214945 = -r6214944;
        return r6214945;
}

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

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

  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 2019119 
(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)))