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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le -3.8184842129845526 \cdot 10^{307} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 4.54382517330943497 \cdot 10^{220}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array}\]

\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}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le -3.8184842129845526 \cdot 10^{307} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 4.54382517330943497 \cdot 10^{220}\right):\\
\;\;\;\;\left(a + z\right) - b\\

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

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r2421539 = x;
        double r2421540 = y;
        double r2421541 = r2421539 + r2421540;
        double r2421542 = z;
        double r2421543 = r2421541 * r2421542;
        double r2421544 = t;
        double r2421545 = r2421544 + r2421540;
        double r2421546 = a;
        double r2421547 = r2421545 * r2421546;
        double r2421548 = r2421543 + r2421547;
        double r2421549 = b;
        double r2421550 = r2421540 * r2421549;
        double r2421551 = r2421548 - r2421550;
        double r2421552 = r2421539 + r2421544;
        double r2421553 = r2421552 + r2421540;
        double r2421554 = r2421551 / r2421553;
        return r2421554;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r2421555 = x;
        double r2421556 = y;
        double r2421557 = r2421555 + r2421556;
        double r2421558 = z;
        double r2421559 = r2421557 * r2421558;
        double r2421560 = t;
        double r2421561 = r2421560 + r2421556;
        double r2421562 = a;
        double r2421563 = r2421561 * r2421562;
        double r2421564 = r2421559 + r2421563;
        double r2421565 = b;
        double r2421566 = r2421556 * r2421565;
        double r2421567 = r2421564 - r2421566;
        double r2421568 = r2421555 + r2421560;
        double r2421569 = r2421568 + r2421556;
        double r2421570 = r2421567 / r2421569;
        double r2421571 = -3.8184842129845526e+307;
        bool r2421572 = r2421570 <= r2421571;
        double r2421573 = 4.543825173309435e+220;
        bool r2421574 = r2421570 <= r2421573;
        double r2421575 = !r2421574;
        bool r2421576 = r2421572 || r2421575;
        double r2421577 = r2421562 + r2421558;
        double r2421578 = r2421577 - r2421565;
        double r2421579 = r2421576 ? r2421578 : r2421570;
        return r2421579;
}

Original	27.0
Target	11.4
Herbie	7.9

Derivation

Split input into 2 regimes
if (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -3.8184842129845526e+307 or 4.543825173309435e+220 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))
1. Initial program 60.7
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Using strategy rm
3. Applied clear-num60.7
  \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}}\]
4. Simplified60.7
  \[\leadsto \frac{1}{\color{blue}{\frac{\left(x + t\right) + y}{\mathsf{fma}\left(z, x + y, \left(t + y\right) \cdot a - y \cdot b\right)}}}\]
5. Taylor expanded around 0 17.4
  \[\leadsto \color{blue}{\left(a + z\right) - b}\]
if -3.8184842129845526e+307 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 4.543825173309435e+220
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 simplification7.9
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le -3.8184842129845526 \cdot 10^{307} \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 4.54382517330943497 \cdot 10^{220}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(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)) < -3.8184842129845526e+307 or 4.543825173309435e+220 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))`

`if -3.8184842129845526e+307 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 4.543825173309435e+220`

Reproduce

In
Out