Average Error: 34.1 → 9.5
Time: 18.3s
Precision: 64
\[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -4.356959927988237168348139414849710212524 \cdot 10^{-56}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \le 3.087668654677018032633364446323411964642 \cdot 10^{130}:\\ \;\;\;\;\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \end{array}\]
\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}
↓
\begin{array}{l}
\mathbf{if}\;b \le -4.356959927988237168348139414849710212524 \cdot 10^{-56}:\\
\;\;\;\;-1 \cdot \frac{c}{b}\\

\mathbf{elif}\;b \le 3.087668654677018032633364446323411964642 \cdot 10^{130}:\\
\;\;\;\;\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}\\

\mathbf{else}:\\
\;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\

\end{array}
double f(double a, double b, double c) {
        double r6228157 = b;
        double r6228158 = -r6228157;
        double r6228159 = r6228157 * r6228157;
        double r6228160 = 4.0;
        double r6228161 = a;
        double r6228162 = c;
        double r6228163 = r6228161 * r6228162;
        double r6228164 = r6228160 * r6228163;
        double r6228165 = r6228159 - r6228164;
        double r6228166 = sqrt(r6228165);
        double r6228167 = r6228158 - r6228166;
        double r6228168 = 2.0;
        double r6228169 = r6228168 * r6228161;
        double r6228170 = r6228167 / r6228169;
        return r6228170;
}
↓
double f(double a, double b, double c) {
        double r6228171 = b;
        double r6228172 = -4.356959927988237e-56;
        bool r6228173 = r6228171 <= r6228172;
        double r6228174 = -1.0;
        double r6228175 = c;
        double r6228176 = r6228175 / r6228171;
        double r6228177 = r6228174 * r6228176;
        double r6228178 = 3.087668654677018e+130;
        bool r6228179 = r6228171 <= r6228178;
        double r6228180 = -r6228171;
        double r6228181 = r6228171 * r6228171;
        double r6228182 = 4.0;
        double r6228183 = a;
        double r6228184 = r6228183 * r6228175;
        double r6228185 = r6228182 * r6228184;
        double r6228186 = r6228181 - r6228185;
        double r6228187 = sqrt(r6228186);
        double r6228188 = r6228180 - r6228187;
        double r6228189 = 1.0;
        double r6228190 = 2.0;
        double r6228191 = r6228190 * r6228183;
        double r6228192 = r6228189 / r6228191;
        double r6228193 = r6228188 * r6228192;
        double r6228194 = 1.0;
        double r6228195 = r6228171 / r6228183;
        double r6228196 = r6228176 - r6228195;
        double r6228197 = r6228194 * r6228196;
        double r6228198 = r6228179 ? r6228193 : r6228197;
        double r6228199 = r6228173 ? r6228177 : r6228198;
        return r6228199;
}

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

Target

Original34.1
Target21.1
Herbie9.5
\[\begin{array}{l} \mathbf{if}\;b \lt 0.0:\\ \;\;\;\;\frac{c}{a \cdot \frac{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -4.356959927988237e-56

    1. Initial program 54.0

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

    2. Taylor expanded around -inf 7.7

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

    if -4.356959927988237e-56 < b < 3.087668654677018e+130

    1. Initial program 12.6

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

    3. Applied div-inv12.8

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

    if 3.087668654677018e+130 < b

    1. Initial program 56.2

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

    2. Taylor expanded around inf 2.4

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

    3. Simplified2.4

      \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification9.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -4.356959927988237168348139414849710212524 \cdot 10^{-56}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \le 3.087668654677018032633364446323411964642 \cdot 10^{130}:\\ \;\;\;\;\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (a b c)
  :name "quadm (p42, negative)"

  :herbie-target
  (if (< b 0.0) (/ c (* a (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))) (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))

  (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))