Average Error: 2.2 → 2.3
Time: 17.4s
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 r333153 = x;
        double r333154 = y;
        double r333155 = r333153 / r333154;
        double r333156 = z;
        double r333157 = t;
        double r333158 = r333156 - r333157;
        double r333159 = r333155 * r333158;
        double r333160 = r333159 + r333157;
        return r333160;
}
↓
double f(double x, double y, double z, double t) {
        double r333161 = t;
        double r333162 = -4.8255593621111334e-288;
        bool r333163 = r333161 <= r333162;
        double r333164 = 4034252.392433282;
        bool r333165 = r333161 <= r333164;
        double r333166 = !r333165;
        bool r333167 = r333163 || r333166;
        double r333168 = x;
        double r333169 = y;
        double r333170 = r333168 / r333169;
        double r333171 = z;
        double r333172 = r333171 - r333161;
        double r333173 = r333170 * r333172;
        double r333174 = r333173 + r333161;
        double r333175 = r333172 / r333169;
        double r333176 = r333168 * r333175;
        double r333177 = r333176 + r333161;
        double r333178 = r333167 ? r333174 : r333177;
        return r333178;
}

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))