Average Error: 6.9 → 3.2
Time: 4.2s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 2.74970591031591711 \cdot 10^{-191} \lor \neg \left(x \le 1.999216315040642 \cdot 10^{-121}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t \cdot z - x}}{x + 1} - \frac{\frac{x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;x \le 2.74970591031591711 \cdot 10^{-191} \lor \neg \left(x \le 1.999216315040642 \cdot 10^{-121}\right):\\
\;\;\;\;\frac{x + y \cdot \frac{z}{t \cdot z - x}}{x + 1} - \frac{\frac{x}{t \cdot z - x}}{x + 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{x + \frac{y}{t}}{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 (((x <= 2.749705910315917e-191) || !(x <= 1.999216315040642e-121))) {
		VAR = ((double) (((double) (((double) (x + ((double) (y * ((double) (z / ((double) (((double) (t * z)) - x)))))))) / ((double) (x + 1.0)))) - ((double) (((double) (x / ((double) (((double) (t * z)) - x)))) / ((double) (x + 1.0))))));
	} else {
		VAR = ((double) (((double) (x + ((double) (y / t)))) / ((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

Original6.9
Target0.3
Herbie3.2
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Split input into 2 regimes

  2. if x < 2.749705910315917e-191 or 1.999216315040642e-121 < x

    1. Initial program 7.0

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

    3. Applied div-sub7.0

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

    4. Applied associate-+r-7.0

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

    5. Applied div-sub7.0

      \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z}{t \cdot z - x}}{x + 1} - \frac{\frac{x}{t \cdot z - x}}{x + 1}}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity7.0

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

    8. Applied times-frac2.0

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

    9. Simplified2.0

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

    if 2.749705910315917e-191 < x < 1.999216315040642e-121

    1. Initial program 6.2

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

    2. Taylor expanded around inf 22.7

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

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 2.74970591031591711 \cdot 10^{-191} \lor \neg \left(x \le 1.999216315040642 \cdot 10^{-121}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t \cdot z - x}}{x + 1} - \frac{\frac{x}{t \cdot z - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020140 
(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)))