Average Error: 26.9 → 17.4
Time: 25.8s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.056234233092987742833440840987461810758 \cdot 10^{100} \lor \neg \left(y \le 2.978107348803194624620710694155470328533 \cdot 10^{206}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \end{array}\]
\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 -3.056234233092987742833440840987461810758 \cdot 10^{100} \lor \neg \left(y \le 2.978107348803194624620710694155470328533 \cdot 10^{206}\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 r727316 = x;
        double r727317 = y;
        double r727318 = r727316 + r727317;
        double r727319 = z;
        double r727320 = r727318 * r727319;
        double r727321 = t;
        double r727322 = r727321 + r727317;
        double r727323 = a;
        double r727324 = r727322 * r727323;
        double r727325 = r727320 + r727324;
        double r727326 = b;
        double r727327 = r727317 * r727326;
        double r727328 = r727325 - r727327;
        double r727329 = r727316 + r727321;
        double r727330 = r727329 + r727317;
        double r727331 = r727328 / r727330;
        return r727331;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r727332 = y;
        double r727333 = -3.0562342330929877e+100;
        bool r727334 = r727332 <= r727333;
        double r727335 = 2.9781073488031946e+206;
        bool r727336 = r727332 <= r727335;
        double r727337 = !r727336;
        bool r727338 = r727334 || r727337;
        double r727339 = a;
        double r727340 = z;
        double r727341 = r727339 + r727340;
        double r727342 = b;
        double r727343 = r727341 - r727342;
        double r727344 = 1.0;
        double r727345 = x;
        double r727346 = t;
        double r727347 = r727345 + r727346;
        double r727348 = r727347 + r727332;
        double r727349 = r727345 + r727332;
        double r727350 = r727349 * r727340;
        double r727351 = r727346 + r727332;
        double r727352 = r727351 * r727339;
        double r727353 = r727350 + r727352;
        double r727354 = r727332 * r727342;
        double r727355 = r727353 - r727354;
        double r727356 = r727348 / r727355;
        double r727357 = r727344 / r727356;
        double r727358 = r727338 ? r727343 : r727357;
        return r727358;
}

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

Original26.9
Target11.2
Herbie17.4
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.581311708415056427521064305370896655752 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.228596430831560895857110658734089400289 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.0562342330929877e+100 or 2.9781073488031946e+206 < y

    1. Initial program 48.0

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

    3. Applied clear-num48.0

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

    4. Taylor expanded around 0 10.1

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

    if -3.0562342330929877e+100 < y < 2.9781073488031946e+206

    1. Initial program 19.8

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

    3. Applied clear-num19.9

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

  4. Final simplification17.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.056234233092987742833440840987461810758 \cdot 10^{100} \lor \neg \left(y \le 2.978107348803194624620710694155470328533 \cdot 10^{206}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(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)) -3.5813117084150564e153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e82) (/ 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)))