Average Error: 34.1 → 10.0
Time: 23.5s
Precision: 64
\[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b_2 \le -4.32337788234514 \cdot 10^{-89}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 5.121074390969514 \cdot 10^{+149}:\\ \;\;\;\;\frac{1}{\frac{a}{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - c \cdot a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]
\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}
↓
\begin{array}{l}
\mathbf{if}\;b_2 \le -4.32337788234514 \cdot 10^{-89}:\\
\;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\

\mathbf{elif}\;b_2 \le 5.121074390969514 \cdot 10^{+149}:\\
\;\;\;\;\frac{1}{\frac{a}{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - c \cdot a}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\

\end{array}
double f(double a, double b_2, double c) {
        double r1995943 = b_2;
        double r1995944 = -r1995943;
        double r1995945 = r1995943 * r1995943;
        double r1995946 = a;
        double r1995947 = c;
        double r1995948 = r1995946 * r1995947;
        double r1995949 = r1995945 - r1995948;
        double r1995950 = sqrt(r1995949);
        double r1995951 = r1995944 - r1995950;
        double r1995952 = r1995951 / r1995946;
        return r1995952;
}
↓
double f(double a, double b_2, double c) {
        double r1995953 = b_2;
        double r1995954 = -4.32337788234514e-89;
        bool r1995955 = r1995953 <= r1995954;
        double r1995956 = -0.5;
        double r1995957 = c;
        double r1995958 = r1995957 / r1995953;
        double r1995959 = r1995956 * r1995958;
        double r1995960 = 5.121074390969514e+149;
        bool r1995961 = r1995953 <= r1995960;
        double r1995962 = 1.0;
        double r1995963 = a;
        double r1995964 = -r1995953;
        double r1995965 = r1995953 * r1995953;
        double r1995966 = r1995957 * r1995963;
        double r1995967 = r1995965 - r1995966;
        double r1995968 = sqrt(r1995967);
        double r1995969 = r1995964 - r1995968;
        double r1995970 = r1995963 / r1995969;
        double r1995971 = r1995962 / r1995970;
        double r1995972 = 0.5;
        double r1995973 = r1995958 * r1995972;
        double r1995974 = 2.0;
        double r1995975 = r1995953 / r1995963;
        double r1995976 = r1995974 * r1995975;
        double r1995977 = r1995973 - r1995976;
        double r1995978 = r1995961 ? r1995971 : r1995977;
        double r1995979 = r1995955 ? r1995959 : r1995978;
        return r1995979;
}

Error

Bits error versus a

Bits error versus b_2

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if b_2 < -4.32337788234514e-89

    1. Initial program 52.3

      \[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

    2. Taylor expanded around -inf 9.2

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{c}{b_2}}\]

    if -4.32337788234514e-89 < b_2 < 5.121074390969514e+149

    1. Initial program 12.3

      \[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity12.3

      \[\leadsto \frac{\left(-b_2\right) - \color{blue}{1 \cdot \sqrt{b_2 \cdot b_2 - a \cdot c}}}{a}\]

    4. Applied *-un-lft-identity12.3

      \[\leadsto \frac{\left(-\color{blue}{1 \cdot b_2}\right) - 1 \cdot \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

    5. Applied distribute-rgt-neg-in12.3

      \[\leadsto \frac{\color{blue}{1 \cdot \left(-b_2\right)} - 1 \cdot \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

    6. Applied distribute-lft-out--12.3

      \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}\right)}}{a}\]

    7. Applied associate-/l*12.4

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}}}\]

    if 5.121074390969514e+149 < b_2

    1. Initial program 59.1

      \[\frac{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

    2. Taylor expanded around inf 2.6

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{c}{b_2} - 2 \cdot \frac{b_2}{a}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;b_2 \le -4.32337788234514 \cdot 10^{-89}:\\ \;\;\;\;\frac{-1}{2} \cdot \frac{c}{b_2}\\ \mathbf{elif}\;b_2 \le 5.121074390969514 \cdot 10^{+149}:\\ \;\;\;\;\frac{1}{\frac{a}{\left(-b_2\right) - \sqrt{b_2 \cdot b_2 - c \cdot a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b_2} \cdot \frac{1}{2} - 2 \cdot \frac{b_2}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019139 
(FPCore (a b_2 c)
  :name "NMSE problem 3.2.1"
  (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))