Average Error: 1.9 → 3.4
Time: 3.3s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.54272324424329845 \cdot 10^{-9} \lor \neg \left(z \le 1.09387645143986444 \cdot 10^{45}\right):\\ \;\;\;\;\left(\left(\frac{x}{y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} + \frac{x}{y} \cdot \left(-t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.54272324424329845 \cdot 10^{-9} \lor \neg \left(z \le 1.09387645143986444 \cdot 10^{45}\right):\\
\;\;\;\;\left(\left(\frac{x}{y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} + \frac{x}{y} \cdot \left(-t\right)\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r435404 = x;
        double r435405 = y;
        double r435406 = r435404 / r435405;
        double r435407 = z;
        double r435408 = t;
        double r435409 = r435407 - r435408;
        double r435410 = r435406 * r435409;
        double r435411 = r435410 + r435408;
        return r435411;
}
↓
double f(double x, double y, double z, double t) {
        double r435412 = z;
        double r435413 = -2.5427232442432984e-09;
        bool r435414 = r435412 <= r435413;
        double r435415 = 1.0938764514398644e+45;
        bool r435416 = r435412 <= r435415;
        double r435417 = !r435416;
        bool r435418 = r435414 || r435417;
        double r435419 = x;
        double r435420 = y;
        double r435421 = r435419 / r435420;
        double r435422 = cbrt(r435412);
        double r435423 = r435422 * r435422;
        double r435424 = r435421 * r435423;
        double r435425 = r435424 * r435422;
        double r435426 = t;
        double r435427 = -r435426;
        double r435428 = r435421 * r435427;
        double r435429 = r435425 + r435428;
        double r435430 = r435429 + r435426;
        double r435431 = r435412 - r435426;
        double r435432 = r435431 / r435420;
        double r435433 = r435419 * r435432;
        double r435434 = r435433 + r435426;
        double r435435 = r435418 ? r435430 : r435434;
        return r435435;
}

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
Target2.2
Herbie3.4
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.5427232442432984e-09 or 1.0938764514398644e+45 < z

    1. Initial program 1.5

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

    3. Applied sub-neg1.5

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

    4. Applied distribute-lft-in1.5

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

    6. Applied add-cube-cbrt2.0

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

    7. Applied associate-*r*2.0

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

    if -2.5427232442432984e-09 < z < 1.0938764514398644e+45

    1. Initial program 2.2

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

    3. Applied div-inv2.3

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

    4. Applied associate-*l*4.4

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

    5. Simplified4.4

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

  4. Final simplification3.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.54272324424329845 \cdot 10^{-9} \lor \neg \left(z \le 1.09387645143986444 \cdot 10^{45}\right):\\ \;\;\;\;\left(\left(\frac{x}{y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z} + \frac{x}{y} \cdot \left(-t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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))