Average Error: 26.1 → 24.2
Time: 7.6s
Precision: binary64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.8636978965541309 \cdot 10^{196}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \le 4.3056053913827381 \cdot 10^{200}:\\ \;\;\;\;\left(z \cdot \left(x + y\right) + \left(t \cdot a + y \cdot \left(a - b\right)\right)\right) \cdot \frac{1}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array}\]
\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}\;x \le -1.8636978965541309 \cdot 10^{196}:\\
\;\;\;\;z\\

\mathbf{elif}\;x \le 4.3056053913827381 \cdot 10^{200}:\\
\;\;\;\;\left(z \cdot \left(x + y\right) + \left(t \cdot a + y \cdot \left(a - b\right)\right)\right) \cdot \frac{1}{x + \left(y + t\right)}\\

\mathbf{else}:\\
\;\;\;\;z\\

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((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 VAR;
	if ((x <= -1.8636978965541309e+196)) {
		VAR = z;
	} else {
		double VAR_1;
		if ((x <= 4.305605391382738e+200)) {
			VAR_1 = ((double) (((double) (((double) (z * ((double) (x + y)))) + ((double) (((double) (t * a)) + ((double) (y * ((double) (a - b)))))))) * ((double) (1.0 / ((double) (x + ((double) (y + t))))))));
		} else {
			VAR_1 = z;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original26.1
Target11.5
Herbie24.2
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt -3.5813117084150564 \cdot 10^{153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \lt 1.2285964308315609 \cdot 10^{82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.8636978965541309e196 or 4.3056053913827381e200 < x

    1. Initial program 37.1

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

    2. Simplified37.1

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

    3. Taylor expanded around inf 25.7

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

    if -1.8636978965541309e196 < x < 4.3056053913827381e200

    1. Initial program 23.8

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

    2. Simplified23.8

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

    4. Applied div-inv23.9

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

  4. Final simplification24.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.8636978965541309 \cdot 10^{196}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \le 4.3056053913827381 \cdot 10^{200}:\\ \;\;\;\;\left(z \cdot \left(x + y\right) + \left(t \cdot a + y \cdot \left(a - b\right)\right)\right) \cdot \frac{1}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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)))