Average Error: 26.2 → 16.1
Time: 6.3s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -7.3254035686044846 \cdot 10^{114} \lor \neg \left(y \le 32.351428127283\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \end{array}\]
\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}\;y \le -7.3254035686044846 \cdot 10^{114} \lor \neg \left(y \le 32.351428127283\right):\\
\;\;\;\;\left(a + z\right) - b\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r748223 = x;
        double r748224 = y;
        double r748225 = r748223 + r748224;
        double r748226 = z;
        double r748227 = r748225 * r748226;
        double r748228 = t;
        double r748229 = r748228 + r748224;
        double r748230 = a;
        double r748231 = r748229 * r748230;
        double r748232 = r748227 + r748231;
        double r748233 = b;
        double r748234 = r748224 * r748233;
        double r748235 = r748232 - r748234;
        double r748236 = r748223 + r748228;
        double r748237 = r748236 + r748224;
        double r748238 = r748235 / r748237;
        return r748238;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r748239 = y;
        double r748240 = -7.325403568604485e+114;
        bool r748241 = r748239 <= r748240;
        double r748242 = 32.351428127283;
        bool r748243 = r748239 <= r748242;
        double r748244 = !r748243;
        bool r748245 = r748241 || r748244;
        double r748246 = a;
        double r748247 = z;
        double r748248 = r748246 + r748247;
        double r748249 = b;
        double r748250 = r748248 - r748249;
        double r748251 = 1.0;
        double r748252 = x;
        double r748253 = t;
        double r748254 = r748252 + r748253;
        double r748255 = r748254 + r748239;
        double r748256 = r748252 + r748239;
        double r748257 = r748256 * r748247;
        double r748258 = r748253 + r748239;
        double r748259 = r748258 * r748246;
        double r748260 = r748257 + r748259;
        double r748261 = r748239 * r748249;
        double r748262 = r748260 - r748261;
        double r748263 = r748255 / r748262;
        double r748264 = r748251 / r748263;
        double r748265 = r748245 ? r748250 : r748264;
        return r748265;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original26.2
Target11.2
Herbie16.1
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.5813117084150564 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.2285964308315609 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -7.325403568604485e+114 or 32.351428127283 < y

    1. Initial program 41.7

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
    2. Using strategy rm

    3. Applied clear-num41.7

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}}\]

    4. Taylor expanded around 0 16.0

      \[\leadsto \color{blue}{\left(a + z\right) - b}\]

    if -7.325403568604485e+114 < y < 32.351428127283

    1. Initial program 16.1

      \[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
    2. Using strategy rm

    3. Applied clear-num16.2

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification16.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7.3254035686044846 \cdot 10^{114} \lor \neg \left(y \le 32.351428127283\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(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)))