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

↓

\[\begin{array}{l} \mathbf{if}\;b \le -2.025649824816678368861606895534923213042 \cdot 10^{153}:\\ \;\;\;\;\left(\frac{c \cdot 1}{b} - 0.5 \cdot \frac{b}{a}\right) - \frac{\frac{b}{2}}{a}\\ \mathbf{elif}\;b \le 3.047677256636077515553757160900796353717 \cdot 10^{-81}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}{2 \cdot a} - \frac{\frac{b}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -1}{b}\\ \end{array}\]

\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 -2.025649824816678368861606895534923213042 \cdot 10^{153}:\\
\;\;\;\;\left(\frac{c \cdot 1}{b} - 0.5 \cdot \frac{b}{a}\right) - \frac{\frac{b}{2}}{a}\\

\mathbf{elif}\;b \le 3.047677256636077515553757160900796353717 \cdot 10^{-81}:\\
\;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}{2 \cdot a} - \frac{\frac{b}{2}}{a}\\

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

\end{array}

double f(double a, double b, double c) {
        double r107114 = b;
        double r107115 = -r107114;
        double r107116 = r107114 * r107114;
        double r107117 = 4.0;
        double r107118 = a;
        double r107119 = r107117 * r107118;
        double r107120 = c;
        double r107121 = r107119 * r107120;
        double r107122 = r107116 - r107121;
        double r107123 = sqrt(r107122);
        double r107124 = r107115 + r107123;
        double r107125 = 2.0;
        double r107126 = r107125 * r107118;
        double r107127 = r107124 / r107126;
        return r107127;
}

↓

double f(double a, double b, double c) {
        double r107128 = b;
        double r107129 = -2.0256498248166784e+153;
        bool r107130 = r107128 <= r107129;
        double r107131 = c;
        double r107132 = 1.0;
        double r107133 = r107131 * r107132;
        double r107134 = r107133 / r107128;
        double r107135 = 0.5;
        double r107136 = a;
        double r107137 = r107128 / r107136;
        double r107138 = r107135 * r107137;
        double r107139 = r107134 - r107138;
        double r107140 = 2.0;
        double r107141 = r107128 / r107140;
        double r107142 = r107141 / r107136;
        double r107143 = r107139 - r107142;
        double r107144 = 3.0476772566360775e-81;
        bool r107145 = r107128 <= r107144;
        double r107146 = r107128 * r107128;
        double r107147 = 4.0;
        double r107148 = r107131 * r107136;
        double r107149 = r107147 * r107148;
        double r107150 = r107146 - r107149;
        double r107151 = sqrt(r107150);
        double r107152 = r107140 * r107136;
        double r107153 = r107151 / r107152;
        double r107154 = r107153 - r107142;
        double r107155 = -1.0;
        double r107156 = r107131 * r107155;
        double r107157 = r107156 / r107128;
        double r107158 = r107145 ? r107154 : r107157;
        double r107159 = r107130 ? r107143 : r107158;
        return r107159;
}

Original	33.8
Target	20.6
Herbie	10.3

Derivation

Split input into 3 regimes
if b < -2.0256498248166784e+153
1. Initial program 63.6
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified63.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied div-sub63.6
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2} - \frac{b}{2}}}{a}\]
5. Applied div-sub63.6
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2}}{a} - \frac{\frac{b}{2}}{a}}\]
6. Simplified63.6
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2}} - \frac{\frac{b}{2}}{a}\]
7. Taylor expanded around -inf 2.0
  \[\leadsto \color{blue}{\left(1 \cdot \frac{c}{b} - 0.5 \cdot \frac{b}{a}\right)} - \frac{\frac{b}{2}}{a}\]
8. Simplified2.0
  \[\leadsto \color{blue}{\left(\frac{c \cdot 1}{b} - \frac{b}{a} \cdot 0.5\right)} - \frac{\frac{b}{2}}{a}\]
if -2.0256498248166784e+153 < b < 3.0476772566360775e-81
1. Initial program 11.9
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified11.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Using strategy rm
4. Applied div-sub11.9
  \[\leadsto \frac{\color{blue}{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2} - \frac{b}{2}}}{a}\]
5. Applied div-sub11.9
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4}}{2}}{a} - \frac{\frac{b}{2}}{a}}\]
6. Simplified11.9
  \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{a \cdot 2}} - \frac{\frac{b}{2}}{a}\]
if 3.0476772566360775e-81 < b
1. Initial program 52.2
  \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\]
2. Simplified52.2
  \[\leadsto \color{blue}{\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}}\]
3. Taylor expanded around inf 10.5
  \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}}\]
4. Simplified10.5
  \[\leadsto \color{blue}{\frac{c \cdot -1}{b}}\]
Recombined 3 regimes into one program.
Final simplification10.3
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.025649824816678368861606895534923213042 \cdot 10^{153}:\\ \;\;\;\;\left(\frac{c \cdot 1}{b} - 0.5 \cdot \frac{b}{a}\right) - \frac{\frac{b}{2}}{a}\\ \mathbf{elif}\;b \le 3.047677256636077515553757160900796353717 \cdot 10^{-81}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - 4 \cdot \left(c \cdot a\right)}}{2 \cdot a} - \frac{\frac{b}{2}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -1}{b}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if b < -2.0256498248166784e+153`

`if -2.0256498248166784e+153 < b < 3.0476772566360775e-81`

`if 3.0476772566360775e-81 < b`

Reproduce

In
Out