Average Error: 52.8 → 6.0
Time: 14.3s
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 r252629 = b;
        double r252630 = -r252629;
        double r252631 = r252629 * r252629;
        double r252632 = 4.0;
        double r252633 = a;
        double r252634 = r252632 * r252633;
        double r252635 = c;
        double r252636 = r252634 * r252635;
        double r252637 = r252631 - r252636;
        double r252638 = sqrt(r252637);
        double r252639 = r252630 + r252638;
        double r252640 = 2.0;
        double r252641 = r252640 * r252633;
        double r252642 = r252639 / r252641;
        return r252642;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r252643 = c;
        double r252644 = -r252643;
        double r252645 = b;
        double r252646 = r252644 / r252645;
        return r252646;
}

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 52.8

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

  2. Simplified52.8

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

  3. Taylor expanded around inf 6.0

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

  4. Simplified6.0

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

  5. Final simplification6.0

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

Reproduce

herbie shell --seed 2019128 
(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)))