Average Error: 2.1 → 1.4
Time: 14.6s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.723193511360802009043525679019870030067 \cdot 10^{-34} \lor \neg \left(x \le 3728411986898782208\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z - t}{\frac{\sqrt[3]{y}}{x}}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.723193511360802009043525679019870030067 \cdot 10^{-34} \lor \neg \left(x \le 3728411986898782208\right):\\
\;\;\;\;\frac{z - t}{y} \cdot x + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r427032 = x;
        double r427033 = y;
        double r427034 = r427032 / r427033;
        double r427035 = z;
        double r427036 = t;
        double r427037 = r427035 - r427036;
        double r427038 = r427034 * r427037;
        double r427039 = r427038 + r427036;
        return r427039;
}
↓
double f(double x, double y, double z, double t) {
        double r427040 = x;
        double r427041 = -4.723193511360802e-34;
        bool r427042 = r427040 <= r427041;
        double r427043 = 3.728411986898782e+18;
        bool r427044 = r427040 <= r427043;
        double r427045 = !r427044;
        bool r427046 = r427042 || r427045;
        double r427047 = z;
        double r427048 = t;
        double r427049 = r427047 - r427048;
        double r427050 = y;
        double r427051 = r427049 / r427050;
        double r427052 = r427051 * r427040;
        double r427053 = r427052 + r427048;
        double r427054 = 1.0;
        double r427055 = cbrt(r427050);
        double r427056 = r427055 * r427055;
        double r427057 = r427054 / r427056;
        double r427058 = r427055 / r427040;
        double r427059 = r427049 / r427058;
        double r427060 = r427057 * r427059;
        double r427061 = r427048 + r427060;
        double r427062 = r427046 ? r427053 : r427061;
        return r427062;
}

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

Original2.1
Target2.3
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -4.723193511360802e-34 or 3.728411986898782e+18 < x

    1. Initial program 3.6

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

    3. Applied div-inv3.6

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

    4. Applied associate-*l*1.9

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

    5. Simplified1.9

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

    if -4.723193511360802e-34 < x < 3.728411986898782e+18

    1. Initial program 1.2

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

    3. Applied add-cube-cbrt1.6

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

    4. Applied *-un-lft-identity1.6

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

    5. Applied times-frac1.6

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

    6. Applied associate-*l*1.0

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

    7. Simplified1.0

      \[\leadsto \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \color{blue}{\frac{z - t}{\frac{\sqrt[3]{y}}{x}}} + t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.723193511360802009043525679019870030067 \cdot 10^{-34} \lor \neg \left(x \le 3728411986898782208\right):\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z - t}{\frac{\sqrt[3]{y}}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"

  :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))