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

↓

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

\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 r70046 = b;
        double r70047 = -r70046;
        double r70048 = r70046 * r70046;
        double r70049 = 4.0;
        double r70050 = a;
        double r70051 = r70049 * r70050;
        double r70052 = c;
        double r70053 = r70051 * r70052;
        double r70054 = r70048 - r70053;
        double r70055 = sqrt(r70054);
        double r70056 = r70047 + r70055;
        double r70057 = 2.0;
        double r70058 = r70057 * r70050;
        double r70059 = r70056 / r70058;
        return r70059;
}

↓

double f(double a, double b, double c) {
        double r70060 = b;
        double r70061 = -2.0256498248166784e+153;
        bool r70062 = r70060 <= r70061;
        double r70063 = c;
        double r70064 = 1.0;
        double r70065 = r70063 * r70064;
        double r70066 = r70065 / r70060;
        double r70067 = 0.5;
        double r70068 = a;
        double r70069 = r70060 / r70068;
        double r70070 = r70067 * r70069;
        double r70071 = r70066 - r70070;
        double r70072 = 2.0;
        double r70073 = r70060 / r70072;
        double r70074 = r70073 / r70068;
        double r70075 = r70071 - r70074;
        double r70076 = 3.0476772566360775e-81;
        bool r70077 = r70060 <= r70076;
        double r70078 = r70060 * r70060;
        double r70079 = 4.0;
        double r70080 = r70063 * r70068;
        double r70081 = r70079 * r70080;
        double r70082 = r70078 - r70081;
        double r70083 = sqrt(r70082);
        double r70084 = r70072 * r70068;
        double r70085 = r70083 / r70084;
        double r70086 = r70085 - r70074;
        double r70087 = -1.0;
        double r70088 = r70063 * r70087;
        double r70089 = r70088 / r70060;
        double r70090 = r70077 ? r70086 : r70089;
        double r70091 = r70062 ? r70075 : r70090;
        return r70091;
}

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