Average Error: 2.2 → 2.7
Time: 20.4s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.491106148705549648049418715852110748345 \cdot 10^{55} \lor \neg \left(t \le 7.655839316478377406918907766774634758489 \cdot 10^{-286}\right):\\ \;\;\;\;\frac{z - t}{\frac{y}{x}} + t\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.491106148705549648049418715852110748345 \cdot 10^{55} \lor \neg \left(t \le 7.655839316478377406918907766774634758489 \cdot 10^{-286}\right):\\
\;\;\;\;\frac{z - t}{\frac{y}{x}} + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r298395 = x;
        double r298396 = y;
        double r298397 = r298395 / r298396;
        double r298398 = z;
        double r298399 = t;
        double r298400 = r298398 - r298399;
        double r298401 = r298397 * r298400;
        double r298402 = r298401 + r298399;
        return r298402;
}
↓
double f(double x, double y, double z, double t) {
        double r298403 = t;
        double r298404 = -3.4911061487055496e+55;
        bool r298405 = r298403 <= r298404;
        double r298406 = 7.655839316478377e-286;
        bool r298407 = r298403 <= r298406;
        double r298408 = !r298407;
        bool r298409 = r298405 || r298408;
        double r298410 = z;
        double r298411 = r298410 - r298403;
        double r298412 = y;
        double r298413 = x;
        double r298414 = r298412 / r298413;
        double r298415 = r298411 / r298414;
        double r298416 = r298415 + r298403;
        double r298417 = r298411 / r298412;
        double r298418 = r298413 * r298417;
        double r298419 = r298403 + r298418;
        double r298420 = r298409 ? r298416 : r298419;
        return r298420;
}

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
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.4911061487055496e+55 or 7.655839316478377e-286 < t

    1. Initial program 1.5

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

    3. Applied pow11.5

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

    4. Applied pow11.5

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

    5. Applied pow-prod-down1.5

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

    6. Simplified1.4

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

    if -3.4911061487055496e+55 < t < 7.655839316478377e-286

    1. Initial program 3.6

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

    3. Applied pow13.6

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

    4. Applied pow13.6

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

    5. Applied pow-prod-down3.6

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

    6. Simplified3.5

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

    7. Taylor expanded around 0 3.9

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

    8. Simplified5.2

      \[\leadsto {\color{blue}{\left(x \cdot \frac{z - t}{y}\right)}}^{1} + t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.491106148705549648049418715852110748345 \cdot 10^{55} \lor \neg \left(t \le 7.655839316478377406918907766774634758489 \cdot 10^{-286}\right):\\ \;\;\;\;\frac{z - t}{\frac{y}{x}} + t\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))