Average Error: 7.3 → 3.5
Time: 17.2s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.674072299293221246331844240569415091421 \cdot 10^{83} \lor \neg \left(z \le 1.959697583035078986869572067149780660864 \cdot 10^{152}\right):\\ \;\;\;\;\frac{-x}{-\left(x + 1\right)} - \frac{\frac{y}{t}}{-\left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.674072299293221246331844240569415091421 \cdot 10^{83} \lor \neg \left(z \le 1.959697583035078986869572067149780660864 \cdot 10^{152}\right):\\
\;\;\;\;\frac{-x}{-\left(x + 1\right)} - \frac{\frac{y}{t}}{-\left(x + 1\right)}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r527341 = x;
        double r527342 = y;
        double r527343 = z;
        double r527344 = r527342 * r527343;
        double r527345 = r527344 - r527341;
        double r527346 = t;
        double r527347 = r527346 * r527343;
        double r527348 = r527347 - r527341;
        double r527349 = r527345 / r527348;
        double r527350 = r527341 + r527349;
        double r527351 = 1.0;
        double r527352 = r527341 + r527351;
        double r527353 = r527350 / r527352;
        return r527353;
}
↓
double f(double x, double y, double z, double t) {
        double r527354 = z;
        double r527355 = -1.6740722992932212e+83;
        bool r527356 = r527354 <= r527355;
        double r527357 = 1.959697583035079e+152;
        bool r527358 = r527354 <= r527357;
        double r527359 = !r527358;
        bool r527360 = r527356 || r527359;
        double r527361 = x;
        double r527362 = -r527361;
        double r527363 = 1.0;
        double r527364 = r527361 + r527363;
        double r527365 = -r527364;
        double r527366 = r527362 / r527365;
        double r527367 = y;
        double r527368 = t;
        double r527369 = r527367 / r527368;
        double r527370 = r527369 / r527365;
        double r527371 = r527366 - r527370;
        double r527372 = 1.0;
        double r527373 = r527368 * r527354;
        double r527374 = r527373 - r527361;
        double r527375 = r527367 * r527354;
        double r527376 = r527375 - r527361;
        double r527377 = r527374 / r527376;
        double r527378 = r527372 / r527377;
        double r527379 = r527361 + r527378;
        double r527380 = r527379 / r527364;
        double r527381 = r527360 ? r527371 : r527380;
        return r527381;
}

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 < -1.6740722992932212e+83 or 1.959697583035079e+152 < z

    1. Initial program 21.1

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

    3. Applied clear-num21.1

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

    5. Applied frac-2neg21.1

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

    6. Simplified21.1

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

    8. Applied div-sub21.1

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

    9. Taylor expanded around inf 8.2

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

    if -1.6740722992932212e+83 < z < 1.959697583035079e+152

    1. Initial program 1.5

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

    3. Applied clear-num1.5

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

  4. Final simplification3.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.674072299293221246331844240569415091421 \cdot 10^{83} \lor \neg \left(z \le 1.959697583035078986869572067149780660864 \cdot 10^{152}\right):\\ \;\;\;\;\frac{-x}{-\left(x + 1\right)} - \frac{\frac{y}{t}}{-\left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t \cdot z - x}{y \cdot z - x}}}{x + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 
(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)))