Average Error: 26.0 → 23.4
Time: 6.3s
Precision: binary64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \leq -1.1293488291686183 \cdot 10^{+138}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.755501149415783 \cdot 10^{+261}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + \left(a \cdot t + y \cdot \left(a - b\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array}\]
\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}\;a \leq -1.1293488291686183 \cdot 10^{+138}:\\
\;\;\;\;a\\

\mathbf{elif}\;a \leq 2.755501149415783 \cdot 10^{+261}:\\
\;\;\;\;\frac{\left(x + y\right) \cdot z + \left(a \cdot t + y \cdot \left(a - b\right)\right)}{x + \left(y + t\right)}\\

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

\end{array}
(FPCore (x y z t a b)
 :precision binary64
 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
↓
(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.1293488291686183e+138)
   a
   (if (<= a 2.755501149415783e+261)
     (/ (+ (* (+ x y) z) (+ (* a t) (* y (- a b)))) (+ x (+ y t)))
     a)))
double code(double x, double y, double z, double t, double a, double b) {
	return (((double) (((double) (((double) (((double) (x + y)) * z)) + ((double) (((double) (t + y)) * a)))) - ((double) (y * b)))) / ((double) (((double) (x + t)) + y)));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -1.1293488291686183e+138)) {
		tmp = a;
	} else {
		double tmp_1;
		if ((a <= 2.755501149415783e+261)) {
			tmp_1 = (((double) (((double) (((double) (x + y)) * z)) + ((double) (((double) (a * t)) + ((double) (y * ((double) (a - b)))))))) / ((double) (x + ((double) (y + t)))));
		} else {
			tmp_1 = a;
		}
		tmp = tmp_1;
	}
	return tmp;
}

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

Original26.0
Target11.4
Herbie23.4
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -1.1293488291686183e138 or 2.7555011494157831e261 < a

    1. Initial program Error: 42.5 bits

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

    2. SimplifiedError: 42.5 bits

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

    3. Taylor expanded around 0 Error: 27.6 bits

      \[\leadsto \color{blue}{a}\]

    if -1.1293488291686183e138 < a < 2.7555011494157831e261

    1. Initial program Error: 22.5 bits

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

    2. SimplifiedError: 22.5 bits

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

  4. Final simplificationError: 23.4 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1293488291686183 \cdot 10^{+138}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 2.755501149415783 \cdot 10^{+261}:\\ \;\;\;\;\frac{\left(x + y\right) \cdot z + \left(a \cdot t + y \cdot \left(a - b\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(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) (/ 1.0 (/ (+ (+ 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)))