Average Error: 2.0 → 1.5
Time: 4.7s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.910237375042319 \cdot 10^{67} \lor \neg \left(y \le 4.0064465433570219 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right) + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.910237375042319 \cdot 10^{67} \lor \neg \left(y \le 4.0064465433570219 \cdot 10^{-49}\right):\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r582654 = x;
        double r582655 = y;
        double r582656 = r582654 / r582655;
        double r582657 = z;
        double r582658 = t;
        double r582659 = r582657 - r582658;
        double r582660 = r582656 * r582659;
        double r582661 = r582660 + r582658;
        return r582661;
}
↓
double f(double x, double y, double z, double t) {
        double r582662 = y;
        double r582663 = -5.910237375042319e+67;
        bool r582664 = r582662 <= r582663;
        double r582665 = 4.006446543357022e-49;
        bool r582666 = r582662 <= r582665;
        double r582667 = !r582666;
        bool r582668 = r582664 || r582667;
        double r582669 = x;
        double r582670 = r582669 / r582662;
        double r582671 = z;
        double r582672 = t;
        double r582673 = r582671 - r582672;
        double r582674 = r582670 * r582673;
        double r582675 = r582674 + r582672;
        double r582676 = r582669 * r582671;
        double r582677 = r582676 / r582662;
        double r582678 = r582672 * r582669;
        double r582679 = r582678 / r582662;
        double r582680 = r582677 - r582679;
        double r582681 = r582680 + r582672;
        double r582682 = r582668 ? r582675 : r582681;
        return r582682;
}

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

Original2.0
Target2.1
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 < -5.910237375042319e+67 or 4.006446543357022e-49 < y

    1. Initial program 0.9

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

    if -5.910237375042319e+67 < y < 4.006446543357022e-49

    1. Initial program 3.6

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

    3. Applied add-cube-cbrt4.3

      \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \sqrt[3]{\frac{x}{y}}\right)} \cdot \left(z - t\right) + t\]

    4. Applied associate-*l*4.3

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{y}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right)} + t\]

    5. Taylor expanded around 0 2.3

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.910237375042319 \cdot 10^{67} \lor \neg \left(y \le 4.0064465433570219 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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))