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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le -6.939662278312858132841061974784859759209 \cdot 10^{305}:\\ \;\;\;\;z\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 9.823560067484486557199205658011723736571 \cdot 10^{276}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array}\]

\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}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le -6.939662278312858132841061974784859759209 \cdot 10^{305}:\\
\;\;\;\;z\\

\mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 9.823560067484486557199205658011723736571 \cdot 10^{276}:\\
\;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\

\mathbf{else}:\\
\;\;\;\;z\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r517356 = x;
        double r517357 = y;
        double r517358 = r517356 + r517357;
        double r517359 = z;
        double r517360 = r517358 * r517359;
        double r517361 = t;
        double r517362 = r517361 + r517357;
        double r517363 = a;
        double r517364 = r517362 * r517363;
        double r517365 = r517360 + r517364;
        double r517366 = b;
        double r517367 = r517357 * r517366;
        double r517368 = r517365 - r517367;
        double r517369 = r517356 + r517361;
        double r517370 = r517369 + r517357;
        double r517371 = r517368 / r517370;
        return r517371;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r517372 = x;
        double r517373 = y;
        double r517374 = r517372 + r517373;
        double r517375 = z;
        double r517376 = r517374 * r517375;
        double r517377 = t;
        double r517378 = r517377 + r517373;
        double r517379 = a;
        double r517380 = r517378 * r517379;
        double r517381 = r517376 + r517380;
        double r517382 = b;
        double r517383 = r517373 * r517382;
        double r517384 = r517381 - r517383;
        double r517385 = r517372 + r517377;
        double r517386 = r517385 + r517373;
        double r517387 = r517384 / r517386;
        double r517388 = -6.939662278312858e+305;
        bool r517389 = r517387 <= r517388;
        double r517390 = 9.823560067484487e+276;
        bool r517391 = r517387 <= r517390;
        double r517392 = r517391 ? r517387 : r517375;
        double r517393 = r517389 ? r517375 : r517392;
        return r517393;
}

Target

Original	26.8
Target	11.1
Herbie	17.1

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.581311708415056427521064305370896655752 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.228596430831560895857110658734089400289 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

Split input into 2 regimes
if (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -6.939662278312858e+305 or 9.823560067484487e+276 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))
1. Initial program 63.1
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Taylor expanded around inf 40.1
  \[\leadsto \color{blue}{z}\]
if -6.939662278312858e+305 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 9.823560067484487e+276
1. Initial program 0.3
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
Recombined 2 regimes into one program.
Final simplification17.1
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le -6.939662278312858132841061974784859759209 \cdot 10^{305}:\\ \;\;\;\;z\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 9.823560067484486557199205658011723736571 \cdot 10^{276}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 
(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)) -3.5813117084150564e153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e82) (/ 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 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -6.939662278312858e+305 or 9.823560067484487e+276 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))`

`if -6.939662278312858e+305 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 9.823560067484487e+276`

Reproduce

In
Out