Average Error: 2.2 → 2.7
Time: 20.3s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.491106148705549648049418715852110748345 \cdot 10^{55} \lor \neg \left(t \le 7.655839316478377406918907766774634758489 \cdot 10^{-286}\right):\\ \;\;\;\;\frac{z - t}{\frac{y}{x}} + t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z - t}{y} \cdot x\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.491106148705549648049418715852110748345 \cdot 10^{55} \lor \neg \left(t \le 7.655839316478377406918907766774634758489 \cdot 10^{-286}\right):\\
\;\;\;\;\frac{z - t}{\frac{y}{x}} + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r341357 = x;
        double r341358 = y;
        double r341359 = r341357 / r341358;
        double r341360 = z;
        double r341361 = t;
        double r341362 = r341360 - r341361;
        double r341363 = r341359 * r341362;
        double r341364 = r341363 + r341361;
        return r341364;
}
↓
double f(double x, double y, double z, double t) {
        double r341365 = t;
        double r341366 = -3.4911061487055496e+55;
        bool r341367 = r341365 <= r341366;
        double r341368 = 7.655839316478377e-286;
        bool r341369 = r341365 <= r341368;
        double r341370 = !r341369;
        bool r341371 = r341367 || r341370;
        double r341372 = z;
        double r341373 = r341372 - r341365;
        double r341374 = y;
        double r341375 = x;
        double r341376 = r341374 / r341375;
        double r341377 = r341373 / r341376;
        double r341378 = r341377 + r341365;
        double r341379 = r341373 / r341374;
        double r341380 = r341379 * r341375;
        double r341381 = r341365 + r341380;
        double r341382 = r341371 ? r341378 : r341381;
        return r341382;
}

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

Original2.2
Target2.4
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.4911061487055496e+55 or 7.655839316478377e-286 < t

    1. Initial program 1.5

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

    3. Applied *-un-lft-identity1.5

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

    4. Applied associate-*l*1.5

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

    5. Simplified1.4

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

    if -3.4911061487055496e+55 < t < 7.655839316478377e-286

    1. Initial program 3.6

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

    3. Applied *-un-lft-identity3.6

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

    4. Applied associate-*l*3.6

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

    5. Simplified3.5

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

    7. Applied associate-/r/5.2

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

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.491106148705549648049418715852110748345 \cdot 10^{55} \lor \neg \left(t \le 7.655839316478377406918907766774634758489 \cdot 10^{-286}\right):\\ \;\;\;\;\frac{z - t}{\frac{y}{x}} + t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z - t}{y} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))