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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -7.668263498157483707441263748528829871939 \cdot 10^{-23}:\\ \;\;\;\;\frac{-1}{1 \cdot \left(\frac{b}{c} - \frac{a}{b}\right)}\\ \mathbf{elif}\;b \le 2.938039658404582626293093928685157937414 \cdot 10^{94}:\\ \;\;\;\;\frac{-1}{\frac{2}{b + \sqrt{\mathsf{fma}\left(c, \left(-a\right) \cdot 4, b \cdot b\right)}} \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(-1\right) \cdot \left(\frac{b}{a} - \frac{c}{b}\right)\\ \end{array}\]

\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 -7.668263498157483707441263748528829871939 \cdot 10^{-23}:\\
\;\;\;\;\frac{-1}{1 \cdot \left(\frac{b}{c} - \frac{a}{b}\right)}\\

\mathbf{elif}\;b \le 2.938039658404582626293093928685157937414 \cdot 10^{94}:\\
\;\;\;\;\frac{-1}{\frac{2}{b + \sqrt{\mathsf{fma}\left(c, \left(-a\right) \cdot 4, b \cdot b\right)}} \cdot a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r105940 = b;
        double r105941 = -r105940;
        double r105942 = r105940 * r105940;
        double r105943 = 4.0;
        double r105944 = a;
        double r105945 = c;
        double r105946 = r105944 * r105945;
        double r105947 = r105943 * r105946;
        double r105948 = r105942 - r105947;
        double r105949 = sqrt(r105948);
        double r105950 = r105941 - r105949;
        double r105951 = 2.0;
        double r105952 = r105951 * r105944;
        double r105953 = r105950 / r105952;
        return r105953;
}

↓

double f(double a, double b, double c) {
        double r105954 = b;
        double r105955 = -7.668263498157484e-23;
        bool r105956 = r105954 <= r105955;
        double r105957 = -1.0;
        double r105958 = 1.0;
        double r105959 = c;
        double r105960 = r105954 / r105959;
        double r105961 = a;
        double r105962 = r105961 / r105954;
        double r105963 = r105960 - r105962;
        double r105964 = r105958 * r105963;
        double r105965 = r105957 / r105964;
        double r105966 = 2.9380396584045826e+94;
        bool r105967 = r105954 <= r105966;
        double r105968 = 2.0;
        double r105969 = -r105961;
        double r105970 = 4.0;
        double r105971 = r105969 * r105970;
        double r105972 = r105954 * r105954;
        double r105973 = fma(r105959, r105971, r105972);
        double r105974 = sqrt(r105973);
        double r105975 = r105954 + r105974;
        double r105976 = r105968 / r105975;
        double r105977 = r105976 * r105961;
        double r105978 = r105957 / r105977;
        double r105979 = -r105958;
        double r105980 = r105954 / r105961;
        double r105981 = r105959 / r105954;
        double r105982 = r105980 - r105981;
        double r105983 = r105979 * r105982;
        double r105984 = r105967 ? r105978 : r105983;
        double r105985 = r105956 ? r105965 : r105984;
        return r105985;
}

Original	34.4
Target	21.0
Herbie	10.8

Derivation

Split input into 3 regimes
if b < -7.668263498157484e-23
1. Initial program 55.0
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified55.0
  \[\leadsto \color{blue}{-\frac{b + \sqrt{\mathsf{fma}\left(\left(-a\right) \cdot c, 4, b \cdot b\right)}}{2 \cdot a}}\]
3. Using strategy rm
4. Applied clear-num55.0
  \[\leadsto -\color{blue}{\frac{1}{\frac{2 \cdot a}{b + \sqrt{\mathsf{fma}\left(\left(-a\right) \cdot c, 4, b \cdot b\right)}}}}\]
5. Simplified55.0
  \[\leadsto -\frac{1}{\color{blue}{\frac{2}{b + \sqrt{\mathsf{fma}\left(c, \left(-a\right) \cdot 4, b \cdot b\right)}} \cdot a}}\]
6. Taylor expanded around -inf 7.0
  \[\leadsto -\frac{1}{\color{blue}{1 \cdot \frac{b}{c} - 1 \cdot \frac{a}{b}}}\]
7. Simplified7.0
  \[\leadsto -\frac{1}{\color{blue}{1 \cdot \left(\frac{b}{c} - \frac{a}{b}\right)}}\]
if -7.668263498157484e-23 < b < 2.9380396584045826e+94
1. Initial program 15.6
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified15.6
  \[\leadsto \color{blue}{-\frac{b + \sqrt{\mathsf{fma}\left(\left(-a\right) \cdot c, 4, b \cdot b\right)}}{2 \cdot a}}\]
3. Using strategy rm
4. Applied clear-num15.7
  \[\leadsto -\color{blue}{\frac{1}{\frac{2 \cdot a}{b + \sqrt{\mathsf{fma}\left(\left(-a\right) \cdot c, 4, b \cdot b\right)}}}}\]
5. Simplified15.8
  \[\leadsto -\frac{1}{\color{blue}{\frac{2}{b + \sqrt{\mathsf{fma}\left(c, \left(-a\right) \cdot 4, b \cdot b\right)}} \cdot a}}\]
if 2.9380396584045826e+94 < b
1. Initial program 46.7
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Simplified46.7
  \[\leadsto \color{blue}{-\frac{b + \sqrt{\mathsf{fma}\left(\left(-a\right) \cdot c, 4, b \cdot b\right)}}{2 \cdot a}}\]
3. Taylor expanded around inf 3.9
  \[\leadsto -\color{blue}{\left(1 \cdot \frac{b}{a} - 1 \cdot \frac{c}{b}\right)}\]
4. Simplified3.9
  \[\leadsto -\color{blue}{\left(\frac{b}{a} - \frac{c}{b}\right) \cdot 1}\]
Recombined 3 regimes into one program.
Final simplification10.8
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -7.668263498157483707441263748528829871939 \cdot 10^{-23}:\\ \;\;\;\;\frac{-1}{1 \cdot \left(\frac{b}{c} - \frac{a}{b}\right)}\\ \mathbf{elif}\;b \le 2.938039658404582626293093928685157937414 \cdot 10^{94}:\\ \;\;\;\;\frac{-1}{\frac{2}{b + \sqrt{\mathsf{fma}\left(c, \left(-a\right) \cdot 4, b \cdot b\right)}} \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(-1\right) \cdot \left(\frac{b}{a} - \frac{c}{b}\right)\\ \end{array}\]

Error

Target

Derivation

`if b < -7.668263498157484e-23`

`if -7.668263498157484e-23 < b < 2.9380396584045826e+94`

`if 2.9380396584045826e+94 < b`

Reproduce