Average Error: 2.2 → 1.5
Time: 3.1s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -7.2999266771936822 \cdot 10^{-146} \lor \neg \left(y \le 2.97553152938948895 \cdot 10^{34}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -7.2999266771936822 \cdot 10^{-146} \lor \neg \left(y \le 2.97553152938948895 \cdot 10^{34}\right):\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r428586 = x;
        double r428587 = y;
        double r428588 = r428586 / r428587;
        double r428589 = z;
        double r428590 = t;
        double r428591 = r428589 - r428590;
        double r428592 = r428588 * r428591;
        double r428593 = r428592 + r428590;
        return r428593;
}
↓
double f(double x, double y, double z, double t) {
        double r428594 = y;
        double r428595 = -7.299926677193682e-146;
        bool r428596 = r428594 <= r428595;
        double r428597 = 2.975531529389489e+34;
        bool r428598 = r428594 <= r428597;
        double r428599 = !r428598;
        bool r428600 = r428596 || r428599;
        double r428601 = x;
        double r428602 = r428601 / r428594;
        double r428603 = z;
        double r428604 = t;
        double r428605 = r428603 - r428604;
        double r428606 = r428602 * r428605;
        double r428607 = r428606 + r428604;
        double r428608 = r428601 * r428605;
        double r428609 = r428608 / r428594;
        double r428610 = r428609 + r428604;
        double r428611 = r428600 ? r428607 : r428610;
        return r428611;
}

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
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -7.299926677193682e-146 or 2.975531529389489e+34 < y

    1. Initial program 1.3

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

    if -7.299926677193682e-146 < y < 2.975531529389489e+34

    1. Initial program 4.3

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

    3. Applied associate-*l/2.2

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7.2999266771936822 \cdot 10^{-146} \lor \neg \left(y \le 2.97553152938948895 \cdot 10^{34}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))