Average Error: 2.0 → 1.5
Time: 14.4s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.4631969570436788 \cdot 10^{58} \lor \neg \left(y \le 3.1486740368353013 \cdot 10^{-100}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.4631969570436788 \cdot 10^{58} \lor \neg \left(y \le 3.1486740368353013 \cdot 10^{-100}\right):\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r552284 = x;
        double r552285 = y;
        double r552286 = r552284 / r552285;
        double r552287 = z;
        double r552288 = t;
        double r552289 = r552287 - r552288;
        double r552290 = r552286 * r552289;
        double r552291 = r552290 + r552288;
        return r552291;
}
↓
double f(double x, double y, double z, double t) {
        double r552292 = y;
        double r552293 = -2.4631969570436788e+58;
        bool r552294 = r552292 <= r552293;
        double r552295 = 3.1486740368353013e-100;
        bool r552296 = r552292 <= r552295;
        double r552297 = !r552296;
        bool r552298 = r552294 || r552297;
        double r552299 = x;
        double r552300 = r552299 / r552292;
        double r552301 = z;
        double r552302 = t;
        double r552303 = r552301 - r552302;
        double r552304 = r552300 * r552303;
        double r552305 = r552304 + r552302;
        double r552306 = r552299 * r552303;
        double r552307 = r552306 / r552292;
        double r552308 = r552307 + r552302;
        double r552309 = r552298 ? r552305 : r552308;
        return r552309;
}

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

Original2.0
Target2.3
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.4631969570436788e+58 or 3.1486740368353013e-100 < y

    1. Initial program 1.1

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

    if -2.4631969570436788e+58 < y < 3.1486740368353013e-100

    1. Initial program 3.6

      \[\frac{x}{y} \cdot \left(z - t\right) + t\]
    2. Using strategy rm

    3. Applied associate-*l/2.1

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.4631969570436788 \cdot 10^{58} \lor \neg \left(y \le 3.1486740368353013 \cdot 10^{-100}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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