Average Error: 26.9 → 17.4
Time: 24.3s
Precision: 64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.056234233092987742833440840987461810758 \cdot 10^{100} \lor \neg \left(y \le 2.978107348803194624620710694155470328533 \cdot 10^{206}\right):\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\\ \end{array}\]
\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}\;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}:\\
\;\;\;\;\left(\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b\right) \cdot \frac{1}{\left(x + t\right) + y}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r789628 = x;
        double r789629 = y;
        double r789630 = r789628 + r789629;
        double r789631 = z;
        double r789632 = r789630 * r789631;
        double r789633 = t;
        double r789634 = r789633 + r789629;
        double r789635 = a;
        double r789636 = r789634 * r789635;
        double r789637 = r789632 + r789636;
        double r789638 = b;
        double r789639 = r789629 * r789638;
        double r789640 = r789637 - r789639;
        double r789641 = r789628 + r789633;
        double r789642 = r789641 + r789629;
        double r789643 = r789640 / r789642;
        return r789643;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r789644 = y;
        double r789645 = -3.0562342330929877e+100;
        bool r789646 = r789644 <= r789645;
        double r789647 = 2.9781073488031946e+206;
        bool r789648 = r789644 <= r789647;
        double r789649 = !r789648;
        bool r789650 = r789646 || r789649;
        double r789651 = a;
        double r789652 = z;
        double r789653 = r789651 + r789652;
        double r789654 = b;
        double r789655 = r789653 - r789654;
        double r789656 = x;
        double r789657 = r789656 + r789644;
        double r789658 = r789657 * r789652;
        double r789659 = t;
        double r789660 = r789659 + r789644;
        double r789661 = r789660 * r789651;
        double r789662 = r789658 + r789661;
        double r789663 = r789644 * r789654;
        double r789664 = r789662 - r789663;
        double r789665 = 1.0;
        double r789666 = r789656 + r789659;
        double r789667 = r789666 + r789644;
        double r789668 = r789665 / r789667;
        double r789669 = r789664 * r789668;
        double r789670 = r789650 ? r789655 : r789669;
        return r789670;
}

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. Simplified48.0

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

    5. 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 div-inv19.9

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

  4. Final simplification17.4

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

Reproduce

herbie shell --seed 2019305 +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)) -3.5813117084150564e153) (- (+ 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)))