Average Error: 7.4 → 3.5
Time: 4.0s
Precision: binary64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -4.5094556256515596 \cdot 10^{+97} \lor \neg \left(z \leq 1.327720719166663 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{z \cdot y - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -4.5094556256515596 \cdot 10^{+97} \lor \neg \left(z \leq 1.327720719166663 \cdot 10^{+93}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{z \cdot y - 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 (<= z -4.5094556256515596e+97) (not (<= z 1.327720719166663e+93)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ 1.0 (/ (- (* z t) x) (- (* z y) 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 ((z <= -4.5094556256515596e+97) || !(z <= 1.327720719166663e+93)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - 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
Target0.4
Herbie3.5
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -4.5094556256515596e97 or 1.3277207191666629e93 < z

    1. Initial program 19.4

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

    2. Taylor expanded around inf 7.8

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

    if -4.5094556256515596e97 < z < 1.3277207191666629e93

    1. Initial program 1.3

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

    3. Applied clear-num_binary641.3

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

    4. Simplified1.3

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5094556256515596 \cdot 10^{+97} \lor \neg \left(z \leq 1.327720719166663 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{z \cdot y - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020220 
(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)))