Average Error: 7.6 → 3.9
Time: 4.9s
Precision: binary64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.50412223857213894 \cdot 10^{192} \lor \neg \left(z \le 1.09136359581078354 \cdot 10^{81}\right):\\ \;\;\;\;\left(x + \frac{y}{t}\right) \cdot \frac{1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.50412223857213894 \cdot 10^{192} \lor \neg \left(z \le 1.09136359581078354 \cdot 10^{81}\right):\\
\;\;\;\;\left(x + \frac{y}{t}\right) \cdot \frac{1}{x + 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{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 (((z <= -3.504122238572139e+192) || !(z <= 1.0913635958107835e+81))) {
		VAR = ((double) (((double) (x + ((double) (y / t)))) * ((double) (1.0 / ((double) (x + 1.0))))));
	} else {
		VAR = ((double) (((double) (x + ((double) (((double) (((double) (y * z)) - x)) * ((double) (1.0 / ((double) (((double) (t * z)) - x)))))))) / ((double) (x + 1.0))));
	}
	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
Herbie3.9
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.50412223857213894e192 or 1.09136359581078354e81 < z

    1. Initial program 21.3

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

    3. Applied div-inv21.4

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

    4. Taylor expanded around inf 7.4

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

    if -3.50412223857213894e192 < z < 1.09136359581078354e81

    1. Initial program 2.5

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

    3. Applied div-inv2.6

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

  4. Final simplification3.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.50412223857213894 \cdot 10^{192} \lor \neg \left(z \le 1.09136359581078354 \cdot 10^{81}\right):\\ \;\;\;\;\left(x + \frac{y}{t}\right) \cdot \frac{1}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020147 
(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)))