Average Error: 2.1 → 2.2
Time: 19.9s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 3.672139456026926873166289334658230039109 \cdot 10^{-268}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t \le 798392594011827.5:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le 3.672139456026926873166289334658230039109 \cdot 10^{-268}:\\
\;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\

\mathbf{elif}\;t \le 798392594011827.5:\\
\;\;\;\;\frac{z - t}{y} \cdot x + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r23664264 = x;
        double r23664265 = y;
        double r23664266 = r23664264 / r23664265;
        double r23664267 = z;
        double r23664268 = t;
        double r23664269 = r23664267 - r23664268;
        double r23664270 = r23664266 * r23664269;
        double r23664271 = r23664270 + r23664268;
        return r23664271;
}
↓
double f(double x, double y, double z, double t) {
        double r23664272 = t;
        double r23664273 = 3.672139456026927e-268;
        bool r23664274 = r23664272 <= r23664273;
        double r23664275 = z;
        double r23664276 = r23664275 - r23664272;
        double r23664277 = x;
        double r23664278 = y;
        double r23664279 = r23664277 / r23664278;
        double r23664280 = r23664276 * r23664279;
        double r23664281 = r23664272 + r23664280;
        double r23664282 = 798392594011827.5;
        bool r23664283 = r23664272 <= r23664282;
        double r23664284 = r23664276 / r23664278;
        double r23664285 = r23664284 * r23664277;
        double r23664286 = r23664285 + r23664272;
        double r23664287 = r23664283 ? r23664286 : r23664281;
        double r23664288 = r23664274 ? r23664281 : r23664287;
        return r23664288;
}

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

Original2.1
Target2.4
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < 3.672139456026927e-268 or 798392594011827.5 < t

    1. Initial program 1.7

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

    if 3.672139456026927e-268 < t < 798392594011827.5

    1. Initial program 3.4

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

    3. Applied div-inv3.4

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

    4. Applied associate-*l*4.0

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

    5. Simplified4.0

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 3.672139456026926873166289334658230039109 \cdot 10^{-268}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;t \le 798392594011827.5:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :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))