Average Error: 1.9 → 1.5
Time: 4.7s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.4868586825074196 \cdot 10^{40}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;y \le 1.301427482476951 \cdot 10^{95}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]
\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{\left(z - t\right) \cdot x}{y} + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r587262 = x;
        double r587263 = y;
        double r587264 = r587262 / r587263;
        double r587265 = z;
        double r587266 = t;
        double r587267 = r587265 - r587266;
        double r587268 = r587264 * r587267;
        double r587269 = r587268 + r587266;
        return r587269;
}
↓
double f(double x, double y, double z, double t) {
        double r587270 = y;
        double r587271 = -3.4868586825074196e+40;
        bool r587272 = r587270 <= r587271;
        double r587273 = x;
        double r587274 = r587273 / r587270;
        double r587275 = z;
        double r587276 = t;
        double r587277 = r587275 - r587276;
        double r587278 = r587274 * r587277;
        double r587279 = r587278 + r587276;
        double r587280 = 1.301427482476951e+95;
        bool r587281 = r587270 <= r587280;
        double r587282 = r587277 * r587273;
        double r587283 = r587282 / r587270;
        double r587284 = r587283 + r587276;
        double r587285 = r587277 / r587270;
        double r587286 = r587273 * r587285;
        double r587287 = r587286 + r587276;
        double r587288 = r587281 ? r587284 : r587287;
        double r587289 = r587272 ? r587279 : r587288;
        return r587289;
}

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-*r*3.5

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

    8. Applied associate-*l*3.4

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

    10. Applied associate-*l/2.6

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

    11. Applied associate-*l/2.6

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

    12. Simplified1.9

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

    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

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

Reproduce

herbie shell --seed 2020027 
(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))