Average Error: 2.0 → 1.5
Time: 4.4s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.910237375042319 \cdot 10^{67} \lor \neg \left(y \le 4.0064465433570219 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right) + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.910237375042319 \cdot 10^{67} \lor \neg \left(y \le 4.0064465433570219 \cdot 10^{-49}\right):\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right) + t\\

\end{array}
double f(double x, double y, double z, double t) {
        double r514377 = x;
        double r514378 = y;
        double r514379 = r514377 / r514378;
        double r514380 = z;
        double r514381 = t;
        double r514382 = r514380 - r514381;
        double r514383 = r514379 * r514382;
        double r514384 = r514383 + r514381;
        return r514384;
}
↓
double f(double x, double y, double z, double t) {
        double r514385 = y;
        double r514386 = -5.910237375042319e+67;
        bool r514387 = r514385 <= r514386;
        double r514388 = 4.006446543357022e-49;
        bool r514389 = r514385 <= r514388;
        double r514390 = !r514389;
        bool r514391 = r514387 || r514390;
        double r514392 = x;
        double r514393 = r514392 / r514385;
        double r514394 = z;
        double r514395 = t;
        double r514396 = r514394 - r514395;
        double r514397 = r514393 * r514396;
        double r514398 = r514397 + r514395;
        double r514399 = r514392 * r514394;
        double r514400 = r514399 / r514385;
        double r514401 = r514395 * r514392;
        double r514402 = r514401 / r514385;
        double r514403 = r514400 - r514402;
        double r514404 = r514403 + r514395;
        double r514405 = r514391 ? r514398 : r514404;
        return r514405;
}

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

Original2.0
Target2.1
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 2 regimes

  2. if y < -5.910237375042319e+67 or 4.006446543357022e-49 < y

    1. Initial program 0.9

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

    if -5.910237375042319e+67 < y < 4.006446543357022e-49

    1. Initial program 3.6

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

    3. Applied add-cube-cbrt4.3

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

    4. Applied associate-*l*4.3

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

    6. Applied add-cube-cbrt4.2

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

    7. Applied *-un-lft-identity4.2

      \[\leadsto \left(\sqrt[3]{\frac{\color{blue}{1 \cdot x}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right) + t\]

    8. Applied times-frac4.2

      \[\leadsto \left(\sqrt[3]{\color{blue}{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{x}{\sqrt[3]{y}}}} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right) + t\]

    9. Applied cbrt-prod4.2

      \[\leadsto \left(\color{blue}{\left(\sqrt[3]{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \sqrt[3]{\frac{x}{\sqrt[3]{y}}}\right)} \cdot \sqrt[3]{\frac{x}{y}}\right) \cdot \left(\sqrt[3]{\frac{x}{y}} \cdot \left(z - t\right)\right) + t\]

    10. Taylor expanded around 0 2.3

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.910237375042319 \cdot 10^{67} \lor \neg \left(y \le 4.0064465433570219 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot z}{y} - \frac{t \cdot x}{y}\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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))