Average Error: 52.8 → 6.0
Time: 1.3m
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 r7915005 = b;
        double r7915006 = -r7915005;
        double r7915007 = r7915005 * r7915005;
        double r7915008 = 4.0;
        double r7915009 = a;
        double r7915010 = r7915008 * r7915009;
        double r7915011 = c;
        double r7915012 = r7915010 * r7915011;
        double r7915013 = r7915007 - r7915012;
        double r7915014 = sqrt(r7915013);
        double r7915015 = r7915006 + r7915014;
        double r7915016 = 2.0;
        double r7915017 = r7915016 * r7915009;
        double r7915018 = r7915015 / r7915017;
        return r7915018;
}
↓
double f(double __attribute__((unused)) a, double b, double c) {
        double r7915019 = c;
        double r7915020 = b;
        double r7915021 = r7915019 / r7915020;
        double r7915022 = -r7915021;
        return r7915022;
}

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)))