Average Error: 27.0 → 13.2
Time: 21.9s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8734976865957546379114971136:\\ \;\;\;\;\left(a + z\right) - \frac{b}{\frac{\left(y + t\right) + x}{y}}\\ \mathbf{elif}\;y \le 4.402135283980321324040881395991840262925 \cdot 10^{55}:\\ \;\;\;\;\frac{1}{\frac{\left(y + t\right) + x}{a \cdot \left(y + t\right) + \left(z \cdot \left(y + x\right) - y \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - \frac{b}{\frac{\left(y + t\right) + x}{y}}\\ \end{array}\]
\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}\;y \le -8734976865957546379114971136:\\
\;\;\;\;\left(a + z\right) - \frac{b}{\frac{\left(y + t\right) + x}{y}}\\

\mathbf{elif}\;y \le 4.402135283980321324040881395991840262925 \cdot 10^{55}:\\
\;\;\;\;\frac{1}{\frac{\left(y + t\right) + x}{a \cdot \left(y + t\right) + \left(z \cdot \left(y + x\right) - y \cdot b\right)}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r44512601 = x;
        double r44512602 = y;
        double r44512603 = r44512601 + r44512602;
        double r44512604 = z;
        double r44512605 = r44512603 * r44512604;
        double r44512606 = t;
        double r44512607 = r44512606 + r44512602;
        double r44512608 = a;
        double r44512609 = r44512607 * r44512608;
        double r44512610 = r44512605 + r44512609;
        double r44512611 = b;
        double r44512612 = r44512602 * r44512611;
        double r44512613 = r44512610 - r44512612;
        double r44512614 = r44512601 + r44512606;
        double r44512615 = r44512614 + r44512602;
        double r44512616 = r44512613 / r44512615;
        return r44512616;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r44512617 = y;
        double r44512618 = -8.734976865957546e+27;
        bool r44512619 = r44512617 <= r44512618;
        double r44512620 = a;
        double r44512621 = z;
        double r44512622 = r44512620 + r44512621;
        double r44512623 = b;
        double r44512624 = t;
        double r44512625 = r44512617 + r44512624;
        double r44512626 = x;
        double r44512627 = r44512625 + r44512626;
        double r44512628 = r44512627 / r44512617;
        double r44512629 = r44512623 / r44512628;
        double r44512630 = r44512622 - r44512629;
        double r44512631 = 4.4021352839803213e+55;
        bool r44512632 = r44512617 <= r44512631;
        double r44512633 = 1.0;
        double r44512634 = r44512620 * r44512625;
        double r44512635 = r44512617 + r44512626;
        double r44512636 = r44512621 * r44512635;
        double r44512637 = r44512617 * r44512623;
        double r44512638 = r44512636 - r44512637;
        double r44512639 = r44512634 + r44512638;
        double r44512640 = r44512627 / r44512639;
        double r44512641 = r44512633 / r44512640;
        double r44512642 = r44512632 ? r44512641 : r44512630;
        double r44512643 = r44512619 ? r44512630 : r44512642;
        return r44512643;
}

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

Original27.0
Target11.5
Herbie13.2
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.581311708415056427521064305370896655752 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.228596430831560895857110658734089400289 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -8.734976865957546e+27 or 4.4021352839803213e+55 < y

    1. Initial program 41.0

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

    2. Simplified41.0

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

    4. Applied associate-+r-41.0

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

    5. Applied div-sub41.0

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

    7. Applied associate-/l*33.3

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

    9. Applied div-inv33.4

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

    10. Taylor expanded around inf 10.4

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

    if -8.734976865957546e+27 < y < 4.4021352839803213e+55

    1. Initial program 15.5

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

    2. Simplified15.5

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

    4. Applied clear-num15.6

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

  4. Final simplification13.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -8734976865957546379114971136:\\ \;\;\;\;\left(a + z\right) - \frac{b}{\frac{\left(y + t\right) + x}{y}}\\ \mathbf{elif}\;y \le 4.402135283980321324040881395991840262925 \cdot 10^{55}:\\ \;\;\;\;\frac{1}{\frac{\left(y + t\right) + x}{a \cdot \left(y + t\right) + \left(z \cdot \left(y + x\right) - y \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - \frac{b}{\frac{\left(y + t\right) + x}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"

  :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) (/ 1.0 (/ (+ (+ 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)))