Average Error: 7.6 → 2.7
Time: 11.1s
Precision: binary64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} = -inf.0:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x \cdot x - 1 \cdot 1} \cdot \left(x - 1\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 1.24672670234708982 \cdot 10^{226}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{y}{t}\right) \cdot \frac{1}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} = -inf.0:\\
\;\;\;\;\frac{x + \frac{y}{t}}{x \cdot x - 1 \cdot 1} \cdot \left(x - 1\right)\\

\mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 1.24672670234708982 \cdot 10^{226}:\\
\;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x + ((double) (((double) (((double) (y * z)) - x)) / ((double) (((double) (t * z)) - x)))))) / ((double) (x + 1.0))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) (((double) (x + ((double) (((double) (((double) (y * z)) - x)) / ((double) (((double) (t * z)) - x)))))) / ((double) (x + 1.0)))) <= -inf.0)) {
		VAR = ((double) (((double) (((double) (x + ((double) (y / t)))) / ((double) (((double) (x * x)) - ((double) (1.0 * 1.0)))))) * ((double) (x - 1.0))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x + ((double) (((double) (((double) (y * z)) - x)) / ((double) (((double) (t * z)) - x)))))) / ((double) (x + 1.0)))) <= 1.2467267023470898e+226)) {
			VAR_1 = ((double) (((double) (x + ((double) (((double) (((double) (y * z)) - x)) * ((double) (1.0 / ((double) (((double) (t * z)) - x)))))))) / ((double) (x + 1.0))));
		} else {
			VAR_1 = ((double) (((double) (x + ((double) (y / t)))) * ((double) (1.0 / ((double) (x + 1.0))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.6
Target0.3
Herbie2.7
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) < -inf.0

    1. Initial program 64.0

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]

    2. Taylor expanded around inf 22.4

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1}\]
    3. Using strategy rm

    4. Applied flip-+30.1

      \[\leadsto \frac{x + \frac{y}{t}}{\color{blue}{\frac{x \cdot x - 1 \cdot 1}{x - 1}}}\]

    5. Applied associate-/r/30.1

      \[\leadsto \color{blue}{\frac{x + \frac{y}{t}}{x \cdot x - 1 \cdot 1} \cdot \left(x - 1\right)}\]

    if -inf.0 < (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)) < 1.24672670234708982e226

    1. Initial program 0.8

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
    2. Using strategy rm

    3. Applied div-inv0.8

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

    if 1.24672670234708982e226 < (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))

    1. Initial program 55.5

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]

    2. Taylor expanded around inf 12.3

      \[\leadsto \frac{x + \color{blue}{\frac{y}{t}}}{x + 1}\]
    3. Using strategy rm

    4. Applied div-inv12.3

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

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} = -inf.0:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x \cdot x - 1 \cdot 1} \cdot \left(x - 1\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \le 1.24672670234708982 \cdot 10^{226}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{y}{t}\right) \cdot \frac{1}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))