Average Error: 2.2 → 2.3
Time: 16.7s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.825559362111133383123602167957975791039 \cdot 10^{-288} \lor \neg \left(t \le 4034252.3924332819879055023193359375\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -4.825559362111133383123602167957975791039 \cdot 10^{-288} \lor \neg \left(t \le 4034252.3924332819879055023193359375\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 r330645 = x;
        double r330646 = y;
        double r330647 = r330645 / r330646;
        double r330648 = z;
        double r330649 = t;
        double r330650 = r330648 - r330649;
        double r330651 = r330647 * r330650;
        double r330652 = r330651 + r330649;
        return r330652;
}
↓
double f(double x, double y, double z, double t) {
        double r330653 = t;
        double r330654 = -4.8255593621111334e-288;
        bool r330655 = r330653 <= r330654;
        double r330656 = 4034252.392433282;
        bool r330657 = r330653 <= r330656;
        double r330658 = !r330657;
        bool r330659 = r330655 || r330658;
        double r330660 = x;
        double r330661 = y;
        double r330662 = r330660 / r330661;
        double r330663 = z;
        double r330664 = r330663 - r330653;
        double r330665 = r330662 * r330664;
        double r330666 = r330665 + r330653;
        double r330667 = r330664 / r330661;
        double r330668 = r330660 * r330667;
        double r330669 = r330668 + r330653;
        double r330670 = r330659 ? r330666 : r330669;
        return r330670;
}

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
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -4.8255593621111334e-288 or 4034252.392433282 < t

    1. Initial program 1.4

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

    if -4.8255593621111334e-288 < t < 4034252.392433282

    1. Initial program 4.1

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

    3. Applied div-inv4.1

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

    4. Applied associate-*l*4.5

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

    5. Simplified4.4

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.825559362111133383123602167957975791039 \cdot 10^{-288} \lor \neg \left(t \le 4034252.3924332819879055023193359375\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(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))