Average Error: 52.6 → 0.1
Time: 18.1s
Precision: 64
\[4.930380657631323783823303533017413935458 \cdot 10^{-32} \lt a \lt 20282409603651670423947251286016 \land 4.930380657631323783823303533017413935458 \cdot 10^{-32} \lt b \lt 20282409603651670423947251286016 \land 4.930380657631323783823303533017413935458 \cdot 10^{-32} \lt c \lt 20282409603651670423947251286016\]
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
↓
\[\frac{\frac{c}{\frac{2}{4}}}{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot 4\right) \cdot a}}\]
\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}
↓
\frac{\frac{c}{\frac{2}{4}}}{\left(-b\right) - \sqrt{b \cdot b - \left(c \cdot 4\right) \cdot a}}
double f(double a, double b, double c) {
        double r28758 = b;
        double r28759 = -r28758;
        double r28760 = r28758 * r28758;
        double r28761 = 4.0;
        double r28762 = a;
        double r28763 = r28761 * r28762;
        double r28764 = c;
        double r28765 = r28763 * r28764;
        double r28766 = r28760 - r28765;
        double r28767 = sqrt(r28766);
        double r28768 = r28759 + r28767;
        double r28769 = 2.0;
        double r28770 = r28769 * r28762;
        double r28771 = r28768 / r28770;
        return r28771;
}
↓
double f(double a, double b, double c) {
        double r28772 = c;
        double r28773 = 2.0;
        double r28774 = 4.0;
        double r28775 = r28773 / r28774;
        double r28776 = r28772 / r28775;
        double r28777 = b;
        double r28778 = -r28777;
        double r28779 = r28777 * r28777;
        double r28780 = r28772 * r28774;
        double r28781 = a;
        double r28782 = r28780 * r28781;
        double r28783 = r28779 - r28782;
        double r28784 = sqrt(r28783);
        double r28785 = r28778 - r28784;
        double r28786 = r28776 / r28785;
        return r28786;
}

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 52.6

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

  3. Applied flip-+52.6

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

  4. Simplified0.4

    \[\leadsto \frac{\frac{\color{blue}{0 + \left(4 \cdot a\right) \cdot c}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\]
  5. Using strategy rm

  6. Applied clear-num0.4

    \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\frac{0 + \left(4 \cdot a\right) \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}}}\]

  7. Simplified0.4

    \[\leadsto \frac{1}{\color{blue}{\left(\frac{2}{4} \cdot \frac{a}{a \cdot c}\right) \cdot \left(\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}\right)}}\]
  8. Using strategy rm

  9. Applied associate-/r*0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{\frac{2}{4} \cdot \frac{a}{a \cdot c}}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}}}\]

  10. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{1 \cdot c}{\frac{2}{4}}}}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}}\]

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(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) (* (* 4.0 a) c)))) (* 2.0 a)))