Average Error: 27.0 → 13.2
Time: 22.8s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -8734976865957546379114971136:\\ \;\;\;\;\left(a + z\right) - \frac{b}{\frac{\left(y + t\right) + x}{y}}\\ \mathbf{elif}\;y \le 4.402135283980321324040881395991840262925 \cdot 10^{55}:\\ \;\;\;\;\frac{1}{\frac{\left(y + t\right) + x}{a \cdot \left(y + t\right) + \left(z \cdot \left(y + x\right) - y \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(a + z\right) - \frac{b}{\frac{\left(y + t\right) + x}{y}}\\ \end{array}\]
\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 r41782648 = x;
        double r41782649 = y;
        double r41782650 = r41782648 + r41782649;
        double r41782651 = z;
        double r41782652 = r41782650 * r41782651;
        double r41782653 = t;
        double r41782654 = r41782653 + r41782649;
        double r41782655 = a;
        double r41782656 = r41782654 * r41782655;
        double r41782657 = r41782652 + r41782656;
        double r41782658 = b;
        double r41782659 = r41782649 * r41782658;
        double r41782660 = r41782657 - r41782659;
        double r41782661 = r41782648 + r41782653;
        double r41782662 = r41782661 + r41782649;
        double r41782663 = r41782660 / r41782662;
        return r41782663;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r41782664 = y;
        double r41782665 = -8.734976865957546e+27;
        bool r41782666 = r41782664 <= r41782665;
        double r41782667 = a;
        double r41782668 = z;
        double r41782669 = r41782667 + r41782668;
        double r41782670 = b;
        double r41782671 = t;
        double r41782672 = r41782664 + r41782671;
        double r41782673 = x;
        double r41782674 = r41782672 + r41782673;
        double r41782675 = r41782674 / r41782664;
        double r41782676 = r41782670 / r41782675;
        double r41782677 = r41782669 - r41782676;
        double r41782678 = 4.4021352839803213e+55;
        bool r41782679 = r41782664 <= r41782678;
        double r41782680 = 1.0;
        double r41782681 = r41782667 * r41782672;
        double r41782682 = r41782664 + r41782673;
        double r41782683 = r41782668 * r41782682;
        double r41782684 = r41782664 * r41782670;
        double r41782685 = r41782683 - r41782684;
        double r41782686 = r41782681 + r41782685;
        double r41782687 = r41782674 / r41782686;
        double r41782688 = r41782680 / r41782687;
        double r41782689 = r41782679 ? r41782688 : r41782677;
        double r41782690 = r41782666 ? r41782677 : r41782689;
        return r41782690;
}

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)))