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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty:\\ \;\;\;\;z\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 2.3074590821258177 \cdot 10^{251}:\\ \;\;\;\;{\left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array}\]

\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} = -\infty:\\
\;\;\;\;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 2.3074590821258177 \cdot 10^{251}:\\
\;\;\;\;{\left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\right)}^{1}\\

\mathbf{else}:\\
\;\;\;\;a\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r766704 = x;
        double r766705 = y;
        double r766706 = r766704 + r766705;
        double r766707 = z;
        double r766708 = r766706 * r766707;
        double r766709 = t;
        double r766710 = r766709 + r766705;
        double r766711 = a;
        double r766712 = r766710 * r766711;
        double r766713 = r766708 + r766712;
        double r766714 = b;
        double r766715 = r766705 * r766714;
        double r766716 = r766713 - r766715;
        double r766717 = r766704 + r766709;
        double r766718 = r766717 + r766705;
        double r766719 = r766716 / r766718;
        return r766719;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r766720 = x;
        double r766721 = y;
        double r766722 = r766720 + r766721;
        double r766723 = z;
        double r766724 = r766722 * r766723;
        double r766725 = t;
        double r766726 = r766725 + r766721;
        double r766727 = a;
        double r766728 = r766726 * r766727;
        double r766729 = r766724 + r766728;
        double r766730 = b;
        double r766731 = r766721 * r766730;
        double r766732 = r766729 - r766731;
        double r766733 = r766720 + r766725;
        double r766734 = r766733 + r766721;
        double r766735 = r766732 / r766734;
        double r766736 = -inf.0;
        bool r766737 = r766735 <= r766736;
        double r766738 = 2.3074590821258177e+251;
        bool r766739 = r766735 <= r766738;
        double r766740 = 1.0;
        double r766741 = pow(r766735, r766740);
        double r766742 = r766739 ? r766741 : r766727;
        double r766743 = r766737 ? r766723 : r766742;
        return r766743;
}

Original	26.6
Target	11.0
Herbie	17.9

Derivation

Split input into 3 regimes
if (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -inf.0
1. Initial program 64.0
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Taylor expanded around inf 40.8
  \[\leadsto \color{blue}{z}\]
if -inf.0 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 2.3074590821258177e+251
1. Initial program 0.3
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Using strategy rm
3. Applied div-inv0.5
  \[\leadsto \color{blue}{\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}}\]
4. Using strategy rm
5. Applied pow10.5
  \[\leadsto \left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \color{blue}{{\left(\frac{1}{\left(x + t\right) + y}\right)}^{1}}\]
6. Applied pow10.5
  \[\leadsto \color{blue}{{\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right)}^{1}} \cdot {\left(\frac{1}{\left(x + t\right) + y}\right)}^{1}\]
7. Applied pow-prod-down0.5
  \[\leadsto \color{blue}{{\left(\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\right)}^{1}}\]
8. Simplified0.3
  \[\leadsto {\color{blue}{\left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\right)}}^{1}\]
if 2.3074590821258177e+251 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))
1. Initial program 61.1
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Taylor expanded around 0 42.4
  \[\leadsto \color{blue}{a}\]
Recombined 3 regimes into one program.
Final simplification17.9
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty:\\ \;\;\;\;z\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 2.3074590821258177 \cdot 10^{251}:\\ \;\;\;\;{\left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -inf.0`

`if -inf.0 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 2.3074590821258177e+251`

`if 2.3074590821258177e+251 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))`

Reproduce

In
Out