Average Error: 2.1 → 1.4
Time: 16.1s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.723193511360802009043525679019870030067 \cdot 10^{-34} \lor \neg \left(x \le 3728411986898782208\right):\\ \;\;\;\;t + \frac{z - t}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z - t}{\frac{\sqrt[3]{y}}{x}} + t\\ \end{array}\]
\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):\\
\;\;\;\;t + \frac{z - t}{y} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r282549 = x;
        double r282550 = y;
        double r282551 = r282549 / r282550;
        double r282552 = z;
        double r282553 = t;
        double r282554 = r282552 - r282553;
        double r282555 = r282551 * r282554;
        double r282556 = r282555 + r282553;
        return r282556;
}
↓
double f(double x, double y, double z, double t) {
        double r282557 = x;
        double r282558 = -4.723193511360802e-34;
        bool r282559 = r282557 <= r282558;
        double r282560 = 3.728411986898782e+18;
        bool r282561 = r282557 <= r282560;
        double r282562 = !r282561;
        bool r282563 = r282559 || r282562;
        double r282564 = t;
        double r282565 = z;
        double r282566 = r282565 - r282564;
        double r282567 = y;
        double r282568 = r282566 / r282567;
        double r282569 = r282568 * r282557;
        double r282570 = r282564 + r282569;
        double r282571 = 1.0;
        double r282572 = cbrt(r282567);
        double r282573 = r282572 * r282572;
        double r282574 = r282571 / r282573;
        double r282575 = r282572 / r282557;
        double r282576 = r282566 / r282575;
        double r282577 = r282574 * r282576;
        double r282578 = r282577 + r282564;
        double r282579 = r282563 ? r282570 : r282578;
        return r282579;
}

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 *-un-lft-identity3.6

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

    4. Applied associate-*l*3.6

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

    5. Simplified2.1

      \[\leadsto 1 \cdot \color{blue}{\frac{x}{\frac{y}{z - t}}} + t\]
    6. Using strategy rm

    7. Applied div-inv2.2

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

    8. Simplified1.9

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

    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

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

Reproduce

herbie shell --seed 2019179 
(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))