Average Error: 2.3 → 2.6
Time: 4.3s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9.3573603142636736 \cdot 10^{-114} \lor \neg \left(z \le 2.10465223580603398 \cdot 10^{-265}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;z \le -9.3573603142636736 \cdot 10^{-114} \lor \neg \left(z \le 2.10465223580603398 \cdot 10^{-265}\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 r582142 = x;
        double r582143 = y;
        double r582144 = r582142 / r582143;
        double r582145 = z;
        double r582146 = t;
        double r582147 = r582145 - r582146;
        double r582148 = r582144 * r582147;
        double r582149 = r582148 + r582146;
        return r582149;
}
↓
double f(double x, double y, double z, double t) {
        double r582150 = z;
        double r582151 = -9.357360314263674e-114;
        bool r582152 = r582150 <= r582151;
        double r582153 = 2.104652235806034e-265;
        bool r582154 = r582150 <= r582153;
        double r582155 = !r582154;
        bool r582156 = r582152 || r582155;
        double r582157 = x;
        double r582158 = y;
        double r582159 = r582157 / r582158;
        double r582160 = t;
        double r582161 = r582150 - r582160;
        double r582162 = r582159 * r582161;
        double r582163 = r582162 + r582160;
        double r582164 = r582161 / r582158;
        double r582165 = r582157 * r582164;
        double r582166 = r582165 + r582160;
        double r582167 = r582156 ? r582163 : r582166;
        return r582167;
}

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

Original2.3
Target2.4
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -9.357360314263674e-114 or 2.104652235806034e-265 < z

    1. Initial program 2.0

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

    if -9.357360314263674e-114 < z < 2.104652235806034e-265

    1. Initial program 3.2

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

    3. Applied div-inv3.2

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

    4. Applied associate-*l*4.8

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

    5. Simplified4.8

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.3573603142636736 \cdot 10^{-114} \lor \neg \left(z \le 2.10465223580603398 \cdot 10^{-265}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(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))