Average Error: 52.1 → 6.5
Time: 16.5s
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 r498481 = b;
        double r498482 = -r498481;
        double r498483 = r498481 * r498481;
        double r498484 = 4.0;
        double r498485 = a;
        double r498486 = r498484 * r498485;
        double r498487 = c;
        double r498488 = r498486 * r498487;
        double r498489 = r498483 - r498488;
        double r498490 = sqrt(r498489);
        double r498491 = r498482 + r498490;
        double r498492 = 2.0;
        double r498493 = r498492 * r498485;
        double r498494 = r498491 / r498493;
        return r498494;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r498495 = c;
        double r498496 = -r498495;
        double r498497 = b;
        double r498498 = r498496 / r498497;
        return r498498;
}

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 52.1

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

  2. Simplified52.1

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

  3. Taylor expanded around inf 6.5

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

  4. Simplified6.5

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

  5. Final simplification6.5

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

Reproduce

herbie shell --seed 2019135 
(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)))