Average Error: 7.4 → 3.5
Time: 6.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.495517031960179583205352214012019609179 \cdot 10^{169} \lor \neg \left(z \le 1.465262131468698121202020890747560702537 \cdot 10^{155}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.495517031960179583205352214012019609179 \cdot 10^{169} \lor \neg \left(z \le 1.465262131468698121202020890747560702537 \cdot 10^{155}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r338726 = x;
        double r338727 = y;
        double r338728 = z;
        double r338729 = r338727 * r338728;
        double r338730 = r338729 - r338726;
        double r338731 = t;
        double r338732 = r338731 * r338728;
        double r338733 = r338732 - r338726;
        double r338734 = r338730 / r338733;
        double r338735 = r338726 + r338734;
        double r338736 = 1.0;
        double r338737 = r338726 + r338736;
        double r338738 = r338735 / r338737;
        return r338738;
}
↓
double f(double x, double y, double z, double t) {
        double r338739 = z;
        double r338740 = -1.4955170319601796e+169;
        bool r338741 = r338739 <= r338740;
        double r338742 = 1.4652621314686981e+155;
        bool r338743 = r338739 <= r338742;
        double r338744 = !r338743;
        bool r338745 = r338741 || r338744;
        double r338746 = x;
        double r338747 = y;
        double r338748 = t;
        double r338749 = r338747 / r338748;
        double r338750 = r338746 + r338749;
        double r338751 = 1.0;
        double r338752 = r338746 + r338751;
        double r338753 = r338750 / r338752;
        double r338754 = 1.0;
        double r338755 = r338747 * r338739;
        double r338756 = r338755 - r338746;
        double r338757 = r338748 * r338739;
        double r338758 = r338757 - r338746;
        double r338759 = r338754 / r338758;
        double r338760 = r338756 * r338759;
        double r338761 = r338746 + r338760;
        double r338762 = r338752 / r338761;
        double r338763 = r338754 / r338762;
        double r338764 = r338745 ? r338753 : r338763;
        return r338764;
}

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 < -1.4955170319601796e+169 or 1.4652621314686981e+155 < z

    1. Initial program 23.6

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

    2. Taylor expanded around inf 5.9

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

    if -1.4955170319601796e+169 < z < 1.4652621314686981e+155

    1. Initial program 2.7

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

    3. Applied clear-num2.7

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

    5. Applied div-inv2.8

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.495517031960179583205352214012019609179 \cdot 10^{169} \lor \neg \left(z \le 1.465262131468698121202020890747560702537 \cdot 10^{155}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019318 
(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)))