Average Error: 7.4 → 2.0
Time: 9.9s
Precision: binary64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -4.980687448045208 \cdot 10^{+287} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 3.678624921963633 \cdot 10^{+302}\right):\\ \;\;\;\;\left(\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\right) - \frac{x}{t \cdot \left(z \cdot \left(x + 1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array}\]
\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}{z \cdot t - x}}{x + 1} \leq -4.980687448045208 \cdot 10^{+287} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 3.678624921963633 \cdot 10^{+302}\right):\\
\;\;\;\;\left(\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\right) - \frac{x}{t \cdot \left(z \cdot \left(x + 1\right)\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\

\end{array}
(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (or (<=
          (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))
          -4.980687448045208e+287)
         (not
          (<=
           (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))
           3.678624921963633e+302)))
   (- (+ (/ x (+ x 1.0)) (/ y (* t (+ x 1.0)))) (/ x (* t (* z (+ x 1.0)))))
   (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}
↓
double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)) <= -4.980687448045208e+287) || !(((x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)) <= 3.678624921963633e+302)) {
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) - (x / (t * (z * (x + 1.0))));
	} else {
		tmp = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

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

Original7.4
Target0.3
Herbie2.0
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -4.9806874480452081e287 or 3.678624921963633e302 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

    1. Initial program 62.1

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

    2. Taylor expanded around inf 12.2

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

    3. Simplified12.2

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

    if -4.9806874480452081e287 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 3.678624921963633e302

    1. Initial program 0.7

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -4.980687448045208 \cdot 10^{+287} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 3.678624921963633 \cdot 10^{+302}\right):\\ \;\;\;\;\left(\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\right) - \frac{x}{t \cdot \left(z \cdot \left(x + 1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2021042 
(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)))