Average Error: 2.2 → 2.4
Time: 39.4s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.949379547519634262898875242093193608455 \cdot 10^{-47}:\\ \;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\ \mathbf{elif}\;t \le 9.442112243134707280154952477861642826064 \cdot 10^{-197}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.949379547519634262898875242093193608455 \cdot 10^{-47}:\\
\;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\

\mathbf{elif}\;t \le 9.442112243134707280154952477861642826064 \cdot 10^{-197}:\\
\;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\

\mathbf{else}:\\
\;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r22076358 = x;
        double r22076359 = y;
        double r22076360 = r22076358 / r22076359;
        double r22076361 = z;
        double r22076362 = t;
        double r22076363 = r22076361 - r22076362;
        double r22076364 = r22076360 * r22076363;
        double r22076365 = r22076364 + r22076362;
        return r22076365;
}
↓
double f(double x, double y, double z, double t) {
        double r22076366 = t;
        double r22076367 = -3.9493795475196343e-47;
        bool r22076368 = r22076366 <= r22076367;
        double r22076369 = z;
        double r22076370 = r22076369 - r22076366;
        double r22076371 = y;
        double r22076372 = x;
        double r22076373 = r22076371 / r22076372;
        double r22076374 = r22076370 / r22076373;
        double r22076375 = r22076366 + r22076374;
        double r22076376 = 9.442112243134707e-197;
        bool r22076377 = r22076366 <= r22076376;
        double r22076378 = r22076372 * r22076370;
        double r22076379 = r22076378 / r22076371;
        double r22076380 = r22076379 + r22076366;
        double r22076381 = r22076377 ? r22076380 : r22076375;
        double r22076382 = r22076368 ? r22076375 : r22076381;
        return r22076382;
}

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

Derivation

  1. Split input into 2 regimes

  2. if t < -3.9493795475196343e-47 or 9.442112243134707e-197 < t

    1. Initial program 0.9

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

    2. Taylor expanded around 0 7.1

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

    3. Simplified0.8

      \[\leadsto \color{blue}{\frac{z - t}{\frac{y}{x}}} + t\]

    if -3.9493795475196343e-47 < t < 9.442112243134707e-197

    1. Initial program 4.9

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

    3. Applied associate-*l/5.4

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.949379547519634262898875242093193608455 \cdot 10^{-47}:\\ \;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\ \mathbf{elif}\;t \le 9.442112243134707280154952477861642826064 \cdot 10^{-197}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(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))