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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -1.339237199229079299889677574983198023934 \cdot 10^{154}:\\ \;\;\;\;\frac{1 \cdot \left(\frac{a \cdot c}{b} - b\right)}{a}\\ \mathbf{elif}\;b \le 1.915204981423677423459982128341604006799 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1 \cdot \frac{a \cdot c}{b}}{a}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;b \le -1.339237199229079299889677574983198023934 \cdot 10^{154}:\\
\;\;\;\;\frac{1 \cdot \left(\frac{a \cdot c}{b} - b\right)}{a}\\

\mathbf{elif}\;b \le 1.915204981423677423459982128341604006799 \cdot 10^{-46}:\\
\;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{2}}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r5827633 = b;
        double r5827634 = -r5827633;
        double r5827635 = r5827633 * r5827633;
        double r5827636 = 4.0;
        double r5827637 = a;
        double r5827638 = r5827636 * r5827637;
        double r5827639 = c;
        double r5827640 = r5827638 * r5827639;
        double r5827641 = r5827635 - r5827640;
        double r5827642 = sqrt(r5827641);
        double r5827643 = r5827634 + r5827642;
        double r5827644 = 2.0;
        double r5827645 = r5827644 * r5827637;
        double r5827646 = r5827643 / r5827645;
        return r5827646;
}

↓

double f(double a, double b, double c) {
        double r5827647 = b;
        double r5827648 = -1.3392371992290793e+154;
        bool r5827649 = r5827647 <= r5827648;
        double r5827650 = 1.0;
        double r5827651 = a;
        double r5827652 = c;
        double r5827653 = r5827651 * r5827652;
        double r5827654 = r5827653 / r5827647;
        double r5827655 = r5827654 - r5827647;
        double r5827656 = r5827650 * r5827655;
        double r5827657 = r5827656 / r5827651;
        double r5827658 = 1.9152049814236774e-46;
        bool r5827659 = r5827647 <= r5827658;
        double r5827660 = r5827647 * r5827647;
        double r5827661 = 4.0;
        double r5827662 = r5827661 * r5827651;
        double r5827663 = r5827652 * r5827662;
        double r5827664 = r5827660 - r5827663;
        double r5827665 = sqrt(r5827664);
        double r5827666 = r5827665 - r5827647;
        double r5827667 = 2.0;
        double r5827668 = r5827666 / r5827667;
        double r5827669 = r5827668 / r5827651;
        double r5827670 = -1.0;
        double r5827671 = r5827670 * r5827654;
        double r5827672 = r5827671 / r5827651;
        double r5827673 = r5827659 ? r5827669 : r5827672;
        double r5827674 = r5827649 ? r5827657 : r5827673;
        return r5827674;
}

Original	34.2
Target	21.0
Herbie	14.6

Derivation

Split input into 3 regimes
if b < -1.3392371992290793e+154
1. Initial program 64.0
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified64.0
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2}}{a}}\]
3. Taylor expanded around -inf 9.5
  \[\leadsto \frac{\color{blue}{1 \cdot \frac{a \cdot c}{b} - 1 \cdot b}}{a}\]
4. Simplified9.5
  \[\leadsto \frac{\color{blue}{1 \cdot \left(\frac{a \cdot c}{b} - b\right)}}{a}\]
if -1.3392371992290793e+154 < b < 1.9152049814236774e-46
1. Initial program 12.8
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified12.8
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied add-cube-cbrt13.1
  \[\leadsto \frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot \color{blue}{\left(\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \sqrt[3]{c}\right)}} - b}{2}}{a}\]
5. Applied associate-*r*13.1
  \[\leadsto \frac{\frac{\sqrt{b \cdot b - \color{blue}{\left(\left(4 \cdot a\right) \cdot \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right)\right) \cdot \sqrt[3]{c}}} - b}{2}}{a}\]
6. Using strategy rm
7. Applied *-un-lft-identity13.1
  \[\leadsto \frac{\frac{\sqrt{b \cdot b - \left(\left(4 \cdot a\right) \cdot \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right)\right) \cdot \sqrt[3]{c}} - \color{blue}{1 \cdot b}}{2}}{a}\]
8. Applied *-un-lft-identity13.1
  \[\leadsto \frac{\frac{\color{blue}{1 \cdot \sqrt{b \cdot b - \left(\left(4 \cdot a\right) \cdot \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right)\right) \cdot \sqrt[3]{c}}} - 1 \cdot b}{2}}{a}\]
9. Applied distribute-lft-out--13.1
  \[\leadsto \frac{\frac{\color{blue}{1 \cdot \left(\sqrt{b \cdot b - \left(\left(4 \cdot a\right) \cdot \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right)\right) \cdot \sqrt[3]{c}} - b\right)}}{2}}{a}\]
10. Simplified12.8
  \[\leadsto \frac{\frac{1 \cdot \color{blue}{\left(\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b\right)}}{2}}{a}\]
if 1.9152049814236774e-46 < b
1. Initial program 54.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified54.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} - b}{2}}{a}}\]
3. Taylor expanded around inf 18.5
  \[\leadsto \frac{\color{blue}{-1 \cdot \frac{a \cdot c}{b}}}{a}\]
Recombined 3 regimes into one program.
Final simplification14.6
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.339237199229079299889677574983198023934 \cdot 10^{154}:\\ \;\;\;\;\frac{1 \cdot \left(\frac{a \cdot c}{b} - b\right)}{a}\\ \mathbf{elif}\;b \le 1.915204981423677423459982128341604006799 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{\sqrt{b \cdot b - c \cdot \left(4 \cdot a\right)} - b}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1 \cdot \frac{a \cdot c}{b}}{a}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -1.3392371992290793e+154`

`if -1.3392371992290793e+154 < b < 1.9152049814236774e-46`

`if 1.9152049814236774e-46 < b`

Reproduce

In
Out