Average Error: 7.3 → 3.5
Time: 24.0s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.222423587555308764778936609441059573037 \cdot 10^{72} \lor \neg \left(z \le 3.067891840168089344532597897815119238015 \cdot 10^{102}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right) \cdot \frac{1}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.222423587555308764778936609441059573037 \cdot 10^{72} \lor \neg \left(z \le 3.067891840168089344532597897815119238015 \cdot 10^{102}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r471518 = x;
        double r471519 = y;
        double r471520 = z;
        double r471521 = r471519 * r471520;
        double r471522 = r471521 - r471518;
        double r471523 = t;
        double r471524 = r471523 * r471520;
        double r471525 = r471524 - r471518;
        double r471526 = r471522 / r471525;
        double r471527 = r471518 + r471526;
        double r471528 = 1.0;
        double r471529 = r471518 + r471528;
        double r471530 = r471527 / r471529;
        return r471530;
}
↓
double f(double x, double y, double z, double t) {
        double r471531 = z;
        double r471532 = -3.2224235875553088e+72;
        bool r471533 = r471531 <= r471532;
        double r471534 = 3.0678918401680893e+102;
        bool r471535 = r471531 <= r471534;
        double r471536 = !r471535;
        bool r471537 = r471533 || r471536;
        double r471538 = x;
        double r471539 = y;
        double r471540 = t;
        double r471541 = r471539 / r471540;
        double r471542 = r471538 + r471541;
        double r471543 = 1.0;
        double r471544 = r471538 + r471543;
        double r471545 = r471542 / r471544;
        double r471546 = r471539 * r471531;
        double r471547 = r471546 - r471538;
        double r471548 = r471540 * r471531;
        double r471549 = r471548 - r471538;
        double r471550 = r471547 / r471549;
        double r471551 = r471538 + r471550;
        double r471552 = 1.0;
        double r471553 = r471552 / r471544;
        double r471554 = r471551 * r471553;
        double r471555 = r471537 ? r471545 : r471554;
        return r471555;
}

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

Original7.3
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 < -3.2224235875553088e+72 or 3.0678918401680893e+102 < z

    1. Initial program 19.3

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

    2. Taylor expanded around inf 8.2

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

    if -3.2224235875553088e+72 < z < 3.0678918401680893e+102

    1. Initial program 0.9

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

    3. Applied div-inv1.0

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.222423587555308764778936609441059573037 \cdot 10^{72} \lor \neg \left(z \le 3.067891840168089344532597897815119238015 \cdot 10^{102}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{y \cdot z - x}{t \cdot z - x}\right) \cdot \frac{1}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))