Average Error: 7.5 → 3.5
Time: 5.1s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.48299927335239672 \cdot 10^{83} \lor \neg \left(z \le 1.42013895838381203 \cdot 10^{77}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.48299927335239672 \cdot 10^{83} \lor \neg \left(z \le 1.42013895838381203 \cdot 10^{77}\right):\\
\;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r757516 = x;
        double r757517 = y;
        double r757518 = z;
        double r757519 = r757517 * r757518;
        double r757520 = r757519 - r757516;
        double r757521 = t;
        double r757522 = r757521 * r757518;
        double r757523 = r757522 - r757516;
        double r757524 = r757520 / r757523;
        double r757525 = r757516 + r757524;
        double r757526 = 1.0;
        double r757527 = r757516 + r757526;
        double r757528 = r757525 / r757527;
        return r757528;
}
↓
double f(double x, double y, double z, double t) {
        double r757529 = z;
        double r757530 = -5.482999273352397e+83;
        bool r757531 = r757529 <= r757530;
        double r757532 = 1.420138958383812e+77;
        bool r757533 = r757529 <= r757532;
        double r757534 = !r757533;
        bool r757535 = r757531 || r757534;
        double r757536 = x;
        double r757537 = y;
        double r757538 = t;
        double r757539 = r757537 / r757538;
        double r757540 = r757536 + r757539;
        double r757541 = 1.0;
        double r757542 = r757536 + r757541;
        double r757543 = r757540 / r757542;
        double r757544 = r757537 * r757529;
        double r757545 = r757544 - r757536;
        double r757546 = 1.0;
        double r757547 = r757538 * r757529;
        double r757548 = r757547 - r757536;
        double r757549 = r757546 / r757548;
        double r757550 = r757545 * r757549;
        double r757551 = r757536 + r757550;
        double r757552 = r757551 / r757542;
        double r757553 = r757535 ? r757543 : r757552;
        return r757553;
}

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

Original7.5
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 < -5.482999273352397e+83 or 1.420138958383812e+77 < z

    1. Initial program 18.8

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

    2. Taylor expanded around inf 8.1

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

    if -5.482999273352397e+83 < z < 1.420138958383812e+77

    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-inv0.9

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.48299927335239672 \cdot 10^{83} \lor \neg \left(z \le 1.42013895838381203 \cdot 10^{77}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z - x\right) \cdot \frac{1}{t \cdot z - x}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 +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)))