Average Error: 7.2 → 3.3
Time: 3.8s
Precision: binary64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -5.66462741609449 \cdot 10^{+83} \lor \neg \left(z \leq 6.106711130237734 \cdot 10^{+106}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(z \cdot y - x\right) \cdot \frac{1}{z \cdot t - x}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -5.66462741609449 \cdot 10^{+83} \lor \neg \left(z \leq 6.106711130237734 \cdot 10^{+106}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \left(z \cdot y - x\right) \cdot \frac{1}{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 (<= z -5.66462741609449e+83) (not (<= z 6.106711130237734e+106)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (* (- (* z y) x) (/ 1.0 (- (* 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 ((z <= -5.66462741609449e+83) || !(z <= 6.106711130237734e+106)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - x) * (1.0 / ((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

Original7.2
Target0.3
Herbie3.3
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.66462741609448964e83 or 6.1067111302377336e106 < z

    1. Initial program 19.7

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

    2. Taylor expanded around inf 7.7

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

    if -5.66462741609448964e83 < z < 6.1067111302377336e106

    1. Initial program 1.0

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

    3. Applied div-inv_binary641.1

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

    4. Simplified1.1

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

  4. Final simplification3.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.66462741609449 \cdot 10^{+83} \lor \neg \left(z \leq 6.106711130237734 \cdot 10^{+106}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(z \cdot y - x\right) \cdot \frac{1}{z \cdot t - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020219 
(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)))