Average Error: 1.9 → 2.1
Time: 14.2s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.874013995062870537512151457622629487895 \cdot 10^{-220} \lor \neg \left(t \le 7.083437615144415838019358577414605267404 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.874013995062870537512151457622629487895 \cdot 10^{-220} \lor \neg \left(t \le 7.083437615144415838019358577414605267404 \cdot 10^{-41}\right):\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r325316 = x;
        double r325317 = y;
        double r325318 = r325316 / r325317;
        double r325319 = z;
        double r325320 = t;
        double r325321 = r325319 - r325320;
        double r325322 = r325318 * r325321;
        double r325323 = r325322 + r325320;
        return r325323;
}
↓
double f(double x, double y, double z, double t) {
        double r325324 = t;
        double r325325 = -2.8740139950628705e-220;
        bool r325326 = r325324 <= r325325;
        double r325327 = 7.083437615144416e-41;
        bool r325328 = r325324 <= r325327;
        double r325329 = !r325328;
        bool r325330 = r325326 || r325329;
        double r325331 = x;
        double r325332 = y;
        double r325333 = r325331 / r325332;
        double r325334 = z;
        double r325335 = r325334 - r325324;
        double r325336 = r325333 * r325335;
        double r325337 = r325336 + r325324;
        double r325338 = r325335 / r325332;
        double r325339 = r325331 * r325338;
        double r325340 = r325339 + r325324;
        double r325341 = r325330 ? r325337 : r325340;
        return r325341;
}

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
Target2.1
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.8740139950628705e-220 or 7.083437615144416e-41 < t

    1. Initial program 0.9

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

    if -2.8740139950628705e-220 < t < 7.083437615144416e-41

    1. Initial program 4.3

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

    3. Applied div-inv4.4

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

    4. Applied associate-*l*5.0

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

    5. Simplified4.9

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.874013995062870537512151457622629487895 \cdot 10^{-220} \lor \neg \left(t \le 7.083437615144415838019358577414605267404 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(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))