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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.933466258714373398674404571719044836719 \cdot 10^{-151}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \le 7.97473148708154202610743994820925403473 \cdot 10^{107}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right) + \left(a \cdot c\right) \cdot \left(\left(-4\right) + 4\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \end{array}\]

\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 -1.933466258714373398674404571719044836719 \cdot 10^{-151}:\\
\;\;\;\;-1 \cdot \frac{c}{b}\\

\mathbf{elif}\;b \le 7.97473148708154202610743994820925403473 \cdot 10^{107}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right) + \left(a \cdot c\right) \cdot \left(\left(-4\right) + 4\right)}}{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 r70014 = b;
        double r70015 = -r70014;
        double r70016 = r70014 * r70014;
        double r70017 = 4.0;
        double r70018 = a;
        double r70019 = c;
        double r70020 = r70018 * r70019;
        double r70021 = r70017 * r70020;
        double r70022 = r70016 - r70021;
        double r70023 = sqrt(r70022);
        double r70024 = r70015 - r70023;
        double r70025 = 2.0;
        double r70026 = r70025 * r70018;
        double r70027 = r70024 / r70026;
        return r70027;
}

↓

double f(double a, double b, double c) {
        double r70028 = b;
        double r70029 = -1.9334662587143734e-151;
        bool r70030 = r70028 <= r70029;
        double r70031 = -1.0;
        double r70032 = c;
        double r70033 = r70032 / r70028;
        double r70034 = r70031 * r70033;
        double r70035 = 7.974731487081542e+107;
        bool r70036 = r70028 <= r70035;
        double r70037 = -r70028;
        double r70038 = 4.0;
        double r70039 = a;
        double r70040 = r70038 * r70039;
        double r70041 = -r70032;
        double r70042 = r70028 * r70028;
        double r70043 = fma(r70040, r70041, r70042);
        double r70044 = r70039 * r70032;
        double r70045 = -r70038;
        double r70046 = r70045 + r70038;
        double r70047 = r70044 * r70046;
        double r70048 = r70043 + r70047;
        double r70049 = sqrt(r70048);
        double r70050 = r70037 - r70049;
        double r70051 = 2.0;
        double r70052 = r70051 * r70039;
        double r70053 = r70050 / r70052;
        double r70054 = 1.0;
        double r70055 = r70028 / r70039;
        double r70056 = r70033 - r70055;
        double r70057 = r70054 * r70056;
        double r70058 = r70036 ? r70053 : r70057;
        double r70059 = r70030 ? r70034 : r70058;
        return r70059;
}

Original	34.9
Target	21.4
Herbie	10.9

Derivation

Split input into 3 regimes
if b < -1.9334662587143734e-151
1. Initial program 50.5
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around -inf 13.2
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
if -1.9334662587143734e-151 < b < 7.974731487081542e+107
1. Initial program 11.4
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied div-inv11.5
  \[\leadsto \color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]
4. Using strategy rm
5. Applied prod-diff11.5
  \[\leadsto \left(\left(-b\right) - \sqrt{\color{blue}{\mathsf{fma}\left(b, b, -\left(a \cdot c\right) \cdot 4\right) + \mathsf{fma}\left(-a \cdot c, 4, \left(a \cdot c\right) \cdot 4\right)}}\right) \cdot \frac{1}{2 \cdot a}\]
6. Simplified11.5
  \[\leadsto \left(\left(-b\right) - \sqrt{\color{blue}{\mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right)} + \mathsf{fma}\left(-a \cdot c, 4, \left(a \cdot c\right) \cdot 4\right)}\right) \cdot \frac{1}{2 \cdot a}\]
7. Simplified11.5
  \[\leadsto \left(\left(-b\right) - \sqrt{\mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right) + \color{blue}{\left(a \cdot c\right) \cdot \left(\left(-4\right) + 4\right)}}\right) \cdot \frac{1}{2 \cdot a}\]
8. Using strategy rm
9. Applied un-div-inv11.4
  \[\leadsto \color{blue}{\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right) + \left(a \cdot c\right) \cdot \left(\left(-4\right) + 4\right)}}{2 \cdot a}}\]
if 7.974731487081542e+107 < b
1. Initial program 49.6
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around inf 3.0
  \[\leadsto \color{blue}{1 \cdot \frac{c}{b} - 1 \cdot \frac{b}{a}}\]
3. Simplified3.0
  \[\leadsto \color{blue}{1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)}\]
Recombined 3 regimes into one program.
Final simplification10.9
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.933466258714373398674404571719044836719 \cdot 10^{-151}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \le 7.97473148708154202610743994820925403473 \cdot 10^{107}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{\mathsf{fma}\left(4 \cdot a, -c, b \cdot b\right) + \left(a \cdot c\right) \cdot \left(\left(-4\right) + 4\right)}}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\frac{c}{b} - \frac{b}{a}\right)\\ \end{array}\]

Error

Target

Derivation

`if b < -1.9334662587143734e-151`

`if -1.9334662587143734e-151 < b < 7.974731487081542e+107`

`if 7.974731487081542e+107 < b`

Reproduce