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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 7.6237735172787151 \cdot 10^{229}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\mathsf{fma}\left(z, x + y, \left(t + y\right) \cdot a - y \cdot b\right)}}\\ \end{array}\]

\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 \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 7.6237735172787151 \cdot 10^{229}\right):\\
\;\;\;\;\left(a + z\right) - b\\

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

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r785693 = x;
        double r785694 = y;
        double r785695 = r785693 + r785694;
        double r785696 = z;
        double r785697 = r785695 * r785696;
        double r785698 = t;
        double r785699 = r785698 + r785694;
        double r785700 = a;
        double r785701 = r785699 * r785700;
        double r785702 = r785697 + r785701;
        double r785703 = b;
        double r785704 = r785694 * r785703;
        double r785705 = r785702 - r785704;
        double r785706 = r785693 + r785698;
        double r785707 = r785706 + r785694;
        double r785708 = r785705 / r785707;
        return r785708;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r785709 = x;
        double r785710 = y;
        double r785711 = r785709 + r785710;
        double r785712 = z;
        double r785713 = r785711 * r785712;
        double r785714 = t;
        double r785715 = r785714 + r785710;
        double r785716 = a;
        double r785717 = r785715 * r785716;
        double r785718 = r785713 + r785717;
        double r785719 = b;
        double r785720 = r785710 * r785719;
        double r785721 = r785718 - r785720;
        double r785722 = r785709 + r785714;
        double r785723 = r785722 + r785710;
        double r785724 = r785721 / r785723;
        double r785725 = -inf.0;
        bool r785726 = r785724 <= r785725;
        double r785727 = 7.623773517278715e+229;
        bool r785728 = r785724 <= r785727;
        double r785729 = !r785728;
        bool r785730 = r785726 || r785729;
        double r785731 = r785716 + r785712;
        double r785732 = r785731 - r785719;
        double r785733 = 1.0;
        double r785734 = r785717 - r785720;
        double r785735 = fma(r785712, r785711, r785734);
        double r785736 = r785723 / r785735;
        double r785737 = r785733 / r785736;
        double r785738 = r785730 ? r785732 : r785737;
        return r785738;
}

Original	26.4
Target	11.4
Herbie	7.9

Derivation

Split input into 2 regimes
if (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -inf.0 or 7.623773517278715e+229 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))
1. Initial program 60.6
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Using strategy rm
3. Applied clear-num60.6
  \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}}\]
4. Simplified60.6
  \[\leadsto \frac{1}{\color{blue}{\frac{\left(x + t\right) + y}{\mathsf{fma}\left(z, x + y, \left(t + y\right) \cdot a - y \cdot b\right)}}}\]
5. Taylor expanded around 0 17.7
  \[\leadsto \color{blue}{\left(a + z\right) - b}\]
if -inf.0 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 7.623773517278715e+229
1. Initial program 0.4
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Using strategy rm
3. Applied clear-num0.5
  \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}}\]
4. Simplified0.5
  \[\leadsto \frac{1}{\color{blue}{\frac{\left(x + t\right) + y}{\mathsf{fma}\left(z, x + y, \left(t + y\right) \cdot a - y \cdot b\right)}}}\]
Recombined 2 regimes into one program.
Final simplification7.9
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 7.6237735172787151 \cdot 10^{229}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\mathsf{fma}\left(z, x + y, \left(t + y\right) \cdot a - y \cdot b\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 +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

Target

Derivation

`if (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -inf.0 or 7.623773517278715e+229 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))`

`if -inf.0 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 7.623773517278715e+229`

Reproduce