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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.569494919068124572690421335939486791404 \cdot 10^{-64}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \le 2.8653816703769607550753035783606354728 \cdot 10^{117}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}}{a} \cdot \frac{1}{2}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a}\\ \end{array}\]

\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 -2.569494919068124572690421335939486791404 \cdot 10^{-64}:\\
\;\;\;\;-1 \cdot \frac{c}{b}\\

\mathbf{elif}\;b \le 2.8653816703769607550753035783606354728 \cdot 10^{117}:\\
\;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}}{a} \cdot \frac{1}{2}\\

\mathbf{else}:\\
\;\;\;\;-1 \cdot \frac{b}{a}\\

\end{array}

double f(double a, double b, double c) {
        double r4070563 = b;
        double r4070564 = -r4070563;
        double r4070565 = r4070563 * r4070563;
        double r4070566 = 4.0;
        double r4070567 = a;
        double r4070568 = c;
        double r4070569 = r4070567 * r4070568;
        double r4070570 = r4070566 * r4070569;
        double r4070571 = r4070565 - r4070570;
        double r4070572 = sqrt(r4070571);
        double r4070573 = r4070564 - r4070572;
        double r4070574 = 2.0;
        double r4070575 = r4070574 * r4070567;
        double r4070576 = r4070573 / r4070575;
        return r4070576;
}

↓

double f(double a, double b, double c) {
        double r4070577 = b;
        double r4070578 = -2.5694949190681246e-64;
        bool r4070579 = r4070577 <= r4070578;
        double r4070580 = -1.0;
        double r4070581 = c;
        double r4070582 = r4070581 / r4070577;
        double r4070583 = r4070580 * r4070582;
        double r4070584 = 2.865381670376961e+117;
        bool r4070585 = r4070577 <= r4070584;
        double r4070586 = -r4070577;
        double r4070587 = r4070577 * r4070577;
        double r4070588 = 4.0;
        double r4070589 = r4070588 * r4070581;
        double r4070590 = a;
        double r4070591 = r4070589 * r4070590;
        double r4070592 = r4070587 - r4070591;
        double r4070593 = sqrt(r4070592);
        double r4070594 = r4070586 - r4070593;
        double r4070595 = r4070594 / r4070590;
        double r4070596 = 1.0;
        double r4070597 = 2.0;
        double r4070598 = r4070596 / r4070597;
        double r4070599 = r4070595 * r4070598;
        double r4070600 = r4070577 / r4070590;
        double r4070601 = r4070580 * r4070600;
        double r4070602 = r4070585 ? r4070599 : r4070601;
        double r4070603 = r4070579 ? r4070583 : r4070602;
        return r4070603;
}

Original	33.8
Target	20.9
Herbie	10.2

Derivation

Split input into 3 regimes
if b < -2.5694949190681246e-64
1. Initial program 53.0
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Taylor expanded around -inf 9.1
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
if -2.5694949190681246e-64 < b < 2.865381670376961e+117
1. Initial program 13.1
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied clear-num13.2
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}\]
4. Using strategy rm
5. Applied *-un-lft-identity13.2
  \[\leadsto \frac{1}{\frac{2 \cdot a}{\color{blue}{1 \cdot \left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right)}}}\]
6. Applied times-frac13.2
  \[\leadsto \frac{1}{\color{blue}{\frac{2}{1} \cdot \frac{a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}\]
7. Applied add-cube-cbrt13.2
  \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{2}{1} \cdot \frac{a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}\]
8. Applied times-frac13.2
  \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{2}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}\]
9. Simplified13.2
  \[\leadsto \color{blue}{\frac{1}{2}} \cdot \frac{\sqrt[3]{1}}{\frac{a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}\]
10. Simplified13.1
  \[\leadsto \frac{1}{2} \cdot \color{blue}{\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}}{a}}\]
if 2.865381670376961e+117 < b
1. Initial program 52.1
  \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
2. Using strategy rm
3. Applied clear-num52.2
  \[\leadsto \color{blue}{\frac{1}{\frac{2 \cdot a}{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}\]
4. Taylor expanded around 0 3.1
  \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}}\]
Recombined 3 regimes into one program.
Final simplification10.2
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.569494919068124572690421335939486791404 \cdot 10^{-64}:\\ \;\;\;\;-1 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \le 2.8653816703769607550753035783606354728 \cdot 10^{117}:\\ \;\;\;\;\frac{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot c\right) \cdot a}}{a} \cdot \frac{1}{2}\\ \mathbf{else}:\\ \;\;\;\;-1 \cdot \frac{b}{a}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -2.5694949190681246e-64`

`if -2.5694949190681246e-64 < b < 2.865381670376961e+117`

`if 2.865381670376961e+117 < b`

Reproduce

In
Out