Average Error: 1.9 → 1.7
Time: 14.3s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.87632604569760037637408890268880098973 \cdot 10^{75} \lor \neg \left(y \le -5.330647358840705908227051774940756230968 \cdot 10^{-307}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{x \cdot z}{y}\right) - \frac{t \cdot x}{y}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.87632604569760037637408890268880098973 \cdot 10^{75} \lor \neg \left(y \le -5.330647358840705908227051774940756230968 \cdot 10^{-307}\right):\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r414341 = x;
        double r414342 = y;
        double r414343 = r414341 / r414342;
        double r414344 = z;
        double r414345 = t;
        double r414346 = r414344 - r414345;
        double r414347 = r414343 * r414346;
        double r414348 = r414347 + r414345;
        return r414348;
}
↓
double f(double x, double y, double z, double t) {
        double r414349 = y;
        double r414350 = -4.8763260456976e+75;
        bool r414351 = r414349 <= r414350;
        double r414352 = -5.330647358840706e-307;
        bool r414353 = r414349 <= r414352;
        double r414354 = !r414353;
        bool r414355 = r414351 || r414354;
        double r414356 = x;
        double r414357 = r414356 / r414349;
        double r414358 = z;
        double r414359 = t;
        double r414360 = r414358 - r414359;
        double r414361 = r414357 * r414360;
        double r414362 = r414361 + r414359;
        double r414363 = r414356 * r414358;
        double r414364 = r414363 / r414349;
        double r414365 = r414359 + r414364;
        double r414366 = r414359 * r414356;
        double r414367 = r414366 / r414349;
        double r414368 = r414365 - r414367;
        double r414369 = r414355 ? r414362 : r414368;
        return r414369;
}

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

Original1.9
Target2.3
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.8763260456976e+75 or -5.330647358840706e-307 < y

    1. Initial program 1.6

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

    if -4.8763260456976e+75 < y < -5.330647358840706e-307

    1. Initial program 2.8

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

    2. Taylor expanded around 0 2.1

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.87632604569760037637408890268880098973 \cdot 10^{75} \lor \neg \left(y \le -5.330647358840705908227051774940756230968 \cdot 10^{-307}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(t + \frac{x \cdot z}{y}\right) - \frac{t \cdot x}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.7594565545626922e-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))