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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 7.49829623920319232 \cdot 10^{267}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{1 \cdot \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array}\]

\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} = -\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 7.49829623920319232 \cdot 10^{267}\right):\\
\;\;\;\;\left(a + z\right) - b\\

\mathbf{else}:\\
\;\;\;\;\frac{1 \cdot \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 r871835 = x;
        double r871836 = y;
        double r871837 = r871835 + r871836;
        double r871838 = z;
        double r871839 = r871837 * r871838;
        double r871840 = t;
        double r871841 = r871840 + r871836;
        double r871842 = a;
        double r871843 = r871841 * r871842;
        double r871844 = r871839 + r871843;
        double r871845 = b;
        double r871846 = r871836 * r871845;
        double r871847 = r871844 - r871846;
        double r871848 = r871835 + r871840;
        double r871849 = r871848 + r871836;
        double r871850 = r871847 / r871849;
        return r871850;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r871851 = x;
        double r871852 = y;
        double r871853 = r871851 + r871852;
        double r871854 = z;
        double r871855 = r871853 * r871854;
        double r871856 = t;
        double r871857 = r871856 + r871852;
        double r871858 = a;
        double r871859 = r871857 * r871858;
        double r871860 = r871855 + r871859;
        double r871861 = b;
        double r871862 = r871852 * r871861;
        double r871863 = r871860 - r871862;
        double r871864 = r871851 + r871856;
        double r871865 = r871864 + r871852;
        double r871866 = r871863 / r871865;
        double r871867 = -inf.0;
        bool r871868 = r871866 <= r871867;
        double r871869 = 7.498296239203192e+267;
        bool r871870 = r871866 <= r871869;
        double r871871 = !r871870;
        bool r871872 = r871868 || r871871;
        double r871873 = r871858 + r871854;
        double r871874 = r871873 - r871861;
        double r871875 = 1.0;
        double r871876 = r871875 * r871860;
        double r871877 = r871876 - r871862;
        double r871878 = r871877 / r871865;
        double r871879 = r871872 ? r871874 : r871878;
        return r871879;
}

Original	26.9
Target	10.8
Herbie	7.3

Derivation

Split input into 2 regimes
if (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < -inf.0 or 7.498296239203192e+267 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))
1. Initial program 62.9
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Using strategy rm
3. Applied clear-num62.9
  \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}}\]
4. Simplified62.9
  \[\leadsto \frac{1}{\color{blue}{\frac{\left(x + t\right) + y}{\mathsf{fma}\left(z, x + y, \left(t + y\right) \cdot a - y \cdot b\right)}}}\]
5. Taylor expanded around 0 16.8
  \[\leadsto \color{blue}{\left(a + z\right) - b}\]
if -inf.0 < (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) < 7.498296239203192e+267
1. Initial program 0.2
  \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
2. Using strategy rm
3. Applied *-un-lft-identity0.2
  \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right)} - y \cdot b}{\left(x + t\right) + y}\]
Recombined 2 regimes into one program.
Final simplification7.3
\[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} = -\infty \lor \neg \left(\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \le 7.49829623920319232 \cdot 10^{267}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{1 \cdot \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020020 +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)) < -inf.0 or 7.498296239203192e+267 < (/ (- (+ (* (+ 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)) < 7.498296239203192e+267`

Reproduce

In
Out