\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]

↓

\[\begin{array}{l} \mathbf{if}\;y \le -1.5789142602105122 \cdot 10^{46} \lor \neg \left(y \le 3.00522161855546254 \cdot 10^{112}\right):\\ \;\;\;\;1 \cdot \left(\left(a + z\right) - b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\\ \end{array}\]

\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}

↓

\begin{array}{l}
\mathbf{if}\;y \le -1.5789142602105122 \cdot 10^{46} \lor \neg \left(y \le 3.00522161855546254 \cdot 10^{112}\right):\\
\;\;\;\;1 \cdot \left(\left(a + z\right) - b\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r1748129 = x;
        double r1748130 = y;
        double r1748131 = r1748129 + r1748130;
        double r1748132 = z;
        double r1748133 = r1748131 * r1748132;
        double r1748134 = t;
        double r1748135 = r1748134 + r1748130;
        double r1748136 = a;
        double r1748137 = r1748135 * r1748136;
        double r1748138 = r1748133 + r1748137;
        double r1748139 = b;
        double r1748140 = r1748130 * r1748139;
        double r1748141 = r1748138 - r1748140;
        double r1748142 = r1748129 + r1748134;
        double r1748143 = r1748142 + r1748130;
        double r1748144 = r1748141 / r1748143;
        return r1748144;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r1748145 = y;
        double r1748146 = -1.5789142602105122e+46;
        bool r1748147 = r1748145 <= r1748146;
        double r1748148 = 3.0052216185554625e+112;
        bool r1748149 = r1748145 <= r1748148;
        double r1748150 = !r1748149;
        bool r1748151 = r1748147 || r1748150;
        double r1748152 = 1.0;
        double r1748153 = a;
        double r1748154 = z;
        double r1748155 = r1748153 + r1748154;
        double r1748156 = b;
        double r1748157 = r1748155 - r1748156;
        double r1748158 = r1748152 * r1748157;
        double r1748159 = x;
        double r1748160 = r1748159 + r1748145;
        double r1748161 = r1748160 * r1748154;
        double r1748162 = t;
        double r1748163 = r1748162 + r1748145;
        double r1748164 = r1748163 * r1748153;
        double r1748165 = r1748161 + r1748164;
        double r1748166 = r1748145 * r1748156;
        double r1748167 = r1748165 - r1748166;
        double r1748168 = r1748159 + r1748162;
        double r1748169 = r1748168 + r1748145;
        double r1748170 = r1748152 / r1748169;
        double r1748171 = r1748167 * r1748170;
        double r1748172 = r1748151 ? r1748158 : r1748171;
        return r1748172;
}

Original	26.9
Target	11.4
Herbie	16.0

Derivation

Split input into 2 regimes
if y < -1.5789142602105122e+46 or 3.0052216185554625e+112 < y
1. Initial program 43.7
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Using strategy rm
3. Applied div-inv43.8
  \[\leadsto \color{blue}{\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}}\]
4. Using strategy rm
5. Applied *-un-lft-identity43.8
  \[\leadsto \color{blue}{\left(1 \cdot \left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right)\right)} \cdot \frac{1}{\left(x + t\right) + y}\]
6. Applied associate-*l*43.8
  \[\leadsto \color{blue}{1 \cdot \left(\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\right)}\]
7. Simplified43.7
  \[\leadsto 1 \cdot \color{blue}{\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}}\]
8. Using strategy rm
9. Applied clear-num43.8
  \[\leadsto 1 \cdot \color{blue}{\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}}\]
10. Taylor expanded around 0 14.3
  \[\leadsto 1 \cdot \color{blue}{\left(\left(a + z\right) - b\right)}\]
if -1.5789142602105122e+46 < y < 3.0052216185554625e+112
1. Initial program 16.9
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Using strategy rm
3. Applied div-inv17.0
  \[\leadsto \color{blue}{\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}}\]
Recombined 2 regimes into one program.
Final simplification16.0
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.5789142602105122 \cdot 10^{46} \lor \neg \left(y \le 3.00522161855546254 \cdot 10^{112}\right):\\ \;\;\;\;1 \cdot \left(\left(a + z\right) - b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b)))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))

Error

Try it out

Target

Derivation

`if y < -1.5789142602105122e+46 or 3.0052216185554625e+112 < y`

`if -1.5789142602105122e+46 < y < 3.0052216185554625e+112`

Reproduce

In
Out