Average Error: 1.9 → 1.5
Time: 5.2s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.4868586825074196 \cdot 10^{40}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;y \le 1.301427482476951 \cdot 10^{95}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.4868586825074196 \cdot 10^{40}:\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

\mathbf{elif}\;y \le 1.301427482476951 \cdot 10^{95}:\\
\;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r394336 = x;
        double r394337 = y;
        double r394338 = r394336 / r394337;
        double r394339 = z;
        double r394340 = t;
        double r394341 = r394339 - r394340;
        double r394342 = r394338 * r394341;
        double r394343 = r394342 + r394340;
        return r394343;
}
↓
double f(double x, double y, double z, double t) {
        double r394344 = y;
        double r394345 = -3.4868586825074196e+40;
        bool r394346 = r394344 <= r394345;
        double r394347 = x;
        double r394348 = r394347 / r394344;
        double r394349 = z;
        double r394350 = t;
        double r394351 = r394349 - r394350;
        double r394352 = r394348 * r394351;
        double r394353 = r394352 + r394350;
        double r394354 = 1.301427482476951e+95;
        bool r394355 = r394344 <= r394354;
        double r394356 = r394347 * r394351;
        double r394357 = r394356 / r394344;
        double r394358 = r394357 + r394350;
        double r394359 = r394351 / r394344;
        double r394360 = r394347 * r394359;
        double r394361 = r394360 + r394350;
        double r394362 = r394355 ? r394358 : r394361;
        double r394363 = r394346 ? r394353 : r394362;
        return r394363;
}

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

Original1.9
Target2.3
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -3.4868586825074196e+40

    1. Initial program 1.0

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

    if -3.4868586825074196e+40 < y < 1.301427482476951e+95

    1. Initial program 2.8

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

    3. Applied add-cube-cbrt3.4

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(\left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right) \cdot \sqrt[3]{z - t}\right)} + t\]

    4. Applied associate-*r*3.5

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot \left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)\right) \cdot \sqrt[3]{z - t}} + t\]
    5. Using strategy rm

    6. Applied associate-*l/2.2

      \[\leadsto \color{blue}{\frac{x \cdot \left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)}{y}} \cdot \sqrt[3]{z - t} + t\]

    7. Applied associate-*l/2.6

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(\sqrt[3]{z - t} \cdot \sqrt[3]{z - t}\right)\right) \cdot \sqrt[3]{z - t}}{y}} + t\]

    8. Simplified1.9

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

    if 1.301427482476951e+95 < y

    1. Initial program 1.1

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

    3. Applied div-inv1.1

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

    4. Applied associate-*l*1.4

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

    5. Simplified1.4

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.4868586825074196 \cdot 10^{40}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;y \le 1.301427482476951 \cdot 10^{95}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(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))