Average Error: 2.1 → 2.2
Time: 20.4s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 3.672139456026926873166289334658230039109 \cdot 10^{-268}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t \le 798392594011827.5:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le 3.672139456026926873166289334658230039109 \cdot 10^{-268}:\\
\;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\

\mathbf{elif}\;t \le 798392594011827.5:\\
\;\;\;\;\frac{z - t}{y} \cdot x + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r19683449 = x;
        double r19683450 = y;
        double r19683451 = r19683449 / r19683450;
        double r19683452 = z;
        double r19683453 = t;
        double r19683454 = r19683452 - r19683453;
        double r19683455 = r19683451 * r19683454;
        double r19683456 = r19683455 + r19683453;
        return r19683456;
}
↓
double f(double x, double y, double z, double t) {
        double r19683457 = t;
        double r19683458 = 3.672139456026927e-268;
        bool r19683459 = r19683457 <= r19683458;
        double r19683460 = z;
        double r19683461 = r19683460 - r19683457;
        double r19683462 = x;
        double r19683463 = y;
        double r19683464 = r19683462 / r19683463;
        double r19683465 = r19683461 * r19683464;
        double r19683466 = r19683457 + r19683465;
        double r19683467 = 798392594011827.5;
        bool r19683468 = r19683457 <= r19683467;
        double r19683469 = r19683461 / r19683463;
        double r19683470 = r19683469 * r19683462;
        double r19683471 = r19683470 + r19683457;
        double r19683472 = r19683468 ? r19683471 : r19683466;
        double r19683473 = r19683459 ? r19683466 : r19683472;
        return r19683473;
}

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

Original2.1
Target2.4
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < 3.672139456026927e-268 or 798392594011827.5 < t

    1. Initial program 1.7

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

    if 3.672139456026927e-268 < t < 798392594011827.5

    1. Initial program 3.4

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

    3. Applied div-inv3.4

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

    4. Applied associate-*l*4.0

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

    5. Simplified4.0

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 3.672139456026926873166289334658230039109 \cdot 10^{-268}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t \le 798392594011827.5:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :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))