Average Error: 2.2 → 1.3
Time: 3.8s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4329597223011.141:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;y \le 2.08341651453868214 \cdot 10^{29}:\\ \;\;\;\;\left(\frac{1}{\frac{y}{x \cdot z}} - \frac{t \cdot x}{y}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{1} \cdot \left(\frac{\sqrt[3]{x}}{y} \cdot \left(z - t\right)\right) + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -4329597223011.141:\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

\mathbf{elif}\;y \le 2.08341651453868214 \cdot 10^{29}:\\
\;\;\;\;\left(\frac{1}{\frac{y}{x \cdot z}} - \frac{t \cdot x}{y}\right) + t\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{1} \cdot \left(\frac{\sqrt[3]{x}}{y} \cdot \left(z - t\right)\right) + t\\

\end{array}
double f(double x, double y, double z, double t) {
        double r382977 = x;
        double r382978 = y;
        double r382979 = r382977 / r382978;
        double r382980 = z;
        double r382981 = t;
        double r382982 = r382980 - r382981;
        double r382983 = r382979 * r382982;
        double r382984 = r382983 + r382981;
        return r382984;
}
↓
double f(double x, double y, double z, double t) {
        double r382985 = y;
        double r382986 = -4329597223011.1406;
        bool r382987 = r382985 <= r382986;
        double r382988 = x;
        double r382989 = r382988 / r382985;
        double r382990 = z;
        double r382991 = t;
        double r382992 = r382990 - r382991;
        double r382993 = r382989 * r382992;
        double r382994 = r382993 + r382991;
        double r382995 = 2.083416514538682e+29;
        bool r382996 = r382985 <= r382995;
        double r382997 = 1.0;
        double r382998 = r382988 * r382990;
        double r382999 = r382985 / r382998;
        double r383000 = r382997 / r382999;
        double r383001 = r382991 * r382988;
        double r383002 = r383001 / r382985;
        double r383003 = r383000 - r383002;
        double r383004 = r383003 + r382991;
        double r383005 = cbrt(r382988);
        double r383006 = r383005 * r383005;
        double r383007 = r383006 / r382997;
        double r383008 = r383005 / r382985;
        double r383009 = r383008 * r382992;
        double r383010 = r383007 * r383009;
        double r383011 = r383010 + r382991;
        double r383012 = r382996 ? r383004 : r383011;
        double r383013 = r382987 ? r382994 : r383012;
        return r383013;
}

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

Derivation

  1. Split input into 3 regimes

  2. if y < -4329597223011.1406

    1. Initial program 1.2

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

    if -4329597223011.1406 < y < 2.083416514538682e+29

    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. Taylor expanded around 0 1.5

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

    7. Applied clear-num1.6

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

    if 2.083416514538682e+29 < y

    1. Initial program 1.1

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

    3. Applied *-un-lft-identity1.1

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

    4. Applied add-cube-cbrt1.5

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

    5. Applied times-frac1.5

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

    6. Applied associate-*l*1.0

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4329597223011.141:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;y \le 2.08341651453868214 \cdot 10^{29}:\\ \;\;\;\;\left(\frac{1}{\frac{y}{x \cdot z}} - \frac{t \cdot x}{y}\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{1} \cdot \left(\frac{\sqrt[3]{x}}{y} \cdot \left(z - t\right)\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 
(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))