Average Error: 7.4 → 3.6
Time: 3.9s
Precision: binary64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -2.399470696119765 \cdot 10^{+69} \lor \neg \left(z \leq 6.859199814445201 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(z \cdot y - x\right) \cdot \frac{1}{z \cdot t - x}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -2.399470696119765 \cdot 10^{+69} \lor \neg \left(z \leq 6.859199814445201 \cdot 10^{+71}\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 -2.399470696119765e+69) (not (<= z 6.859199814445201e+71)))
   (/ (+ 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 (((double) (x + (((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 <= -2.399470696119765e+69) || !(z <= 6.859199814445201e+71))) {
		VAR = (((double) (x + (y / t))) / ((double) (x + 1.0)));
	} else {
		VAR = (((double) (x + ((double) (((double) (((double) (z * y)) - x)) * (1.0 / ((double) (((double) (z * t)) - 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

Original7.4
Target0.4
Herbie3.6
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.39947069611976501e69 or 6.85919981444520093e71 < z

    1. Initial program 18.6

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

    2. Taylor expanded around inf 8.3

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

    if -2.39947069611976501e69 < z < 6.85919981444520093e71

    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

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

    4. Simplified0.8

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

  4. Final simplification3.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.399470696119765 \cdot 10^{+69} \lor \neg \left(z \leq 6.859199814445201 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(z \cdot y - x\right) \cdot \frac{1}{z \cdot t - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020198 
(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)))