Average Error: 26.5 → 19.2
Time: 7.0s
Precision: binary64
\[\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \leq -3.932315982784723 \cdot 10^{+177} \lor \neg \left(a \leq 1.3617675594481185 \cdot 10^{+159}\right):\\ \;\;\;\;a - \frac{y}{x + \left(y + t\right)} \cdot b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + x\right) \cdot z + a \cdot \left(y + t\right)}{x + \left(y + t\right)} + b \cdot \left(y \cdot \frac{-1}{x + \left(y + t\right)}\right)\\ \end{array}\]
\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 -3.932315982784723 \cdot 10^{+177} \lor \neg \left(a \leq 1.3617675594481185 \cdot 10^{+159}\right):\\
\;\;\;\;a - \frac{y}{x + \left(y + t\right)} \cdot b\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(y + x\right) \cdot z + a \cdot \left(y + t\right)}{x + \left(y + t\right)} + b \cdot \left(y \cdot \frac{-1}{x + \left(y + t\right)}\right)\\

\end{array}
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 VAR;
	if (((a <= -3.932315982784723e+177) || !(a <= 1.3617675594481185e+159))) {
		VAR = ((double) (a - ((double) ((y / ((double) (x + ((double) (y + t))))) * b))));
	} else {
		VAR = ((double) ((((double) (((double) (((double) (y + x)) * z)) + ((double) (a * ((double) (y + t)))))) / ((double) (x + ((double) (y + t))))) + ((double) (b * ((double) (y * (-1.0 / ((double) (x + ((double) (y + t)))))))))));
	}
	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

Original26.5
Target11.4
Herbie19.2
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -3.9323159827847228e177 or 1.3617675594481185e159 < a

    1. Initial program 43.5

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

    3. Applied div-sub43.5

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

    4. Simplified43.5

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

    5. Simplified43.2

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

    6. Taylor expanded around 0 23.3

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

    if -3.9323159827847228e177 < a < 1.3617675594481185e159

    1. Initial program 21.7

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

    3. Applied div-sub21.7

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

    4. Simplified21.7

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

    5. Simplified18.0

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

    7. Applied div-inv18.0

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

  4. Final simplification19.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.932315982784723 \cdot 10^{+177} \lor \neg \left(a \leq 1.3617675594481185 \cdot 10^{+159}\right):\\ \;\;\;\;a - \frac{y}{x + \left(y + t\right)} \cdot b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + x\right) \cdot z + a \cdot \left(y + t\right)}{x + \left(y + t\right)} + b \cdot \left(y \cdot \frac{-1}{x + \left(y + t\right)}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(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)))