Average Error: 2.1 → 1.4
Time: 3.5s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.9620127211574489 \cdot 10^{-52}:\\ \;\;\;\;\frac{x \cdot \frac{z - t}{y}}{1} + t\\ \mathbf{elif}\;y \le 413419.115221004875:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{1} \cdot \left(\frac{\sqrt[3]{x}}{y} \cdot \left(z - t\right)\right) + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.9620127211574489 \cdot 10^{-52}:\\
\;\;\;\;\frac{x \cdot \frac{z - t}{y}}{1} + t\\

\mathbf{elif}\;y \le 413419.115221004875:\\
\;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + 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 r506728 = x;
        double r506729 = y;
        double r506730 = r506728 / r506729;
        double r506731 = z;
        double r506732 = t;
        double r506733 = r506731 - r506732;
        double r506734 = r506730 * r506733;
        double r506735 = r506734 + r506732;
        return r506735;
}
↓
double f(double x, double y, double z, double t) {
        double r506736 = y;
        double r506737 = -5.962012721157449e-52;
        bool r506738 = r506736 <= r506737;
        double r506739 = x;
        double r506740 = z;
        double r506741 = t;
        double r506742 = r506740 - r506741;
        double r506743 = r506742 / r506736;
        double r506744 = r506739 * r506743;
        double r506745 = 1.0;
        double r506746 = r506744 / r506745;
        double r506747 = r506746 + r506741;
        double r506748 = 413419.1152210049;
        bool r506749 = r506736 <= r506748;
        double r506750 = r506739 * r506742;
        double r506751 = r506750 / r506736;
        double r506752 = r506751 + r506741;
        double r506753 = cbrt(r506739);
        double r506754 = r506753 * r506753;
        double r506755 = r506754 / r506745;
        double r506756 = r506753 / r506736;
        double r506757 = r506756 * r506742;
        double r506758 = r506755 * r506757;
        double r506759 = r506758 + r506741;
        double r506760 = r506749 ? r506752 : r506759;
        double r506761 = r506738 ? r506747 : r506760;
        return r506761;
}

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

Derivation

  1. Split input into 3 regimes

  2. if y < -5.962012721157449e-52

    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*0.8

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

    8. Applied associate-*l/0.8

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

    9. Simplified1.3

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

    if -5.962012721157449e-52 < y < 413419.1152210049

    1. Initial program 3.9

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

    3. Applied associate-*l/1.9

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

    if 413419.1152210049 < y

    1. Initial program 1.2

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

    3. Applied *-un-lft-identity1.2

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

    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*0.9

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.9620127211574489 \cdot 10^{-52}:\\ \;\;\;\;\frac{x \cdot \frac{z - t}{y}}{1} + t\\ \mathbf{elif}\;y \le 413419.115221004875:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{1} \cdot \left(\frac{\sqrt[3]{x}}{y} \cdot \left(z - t\right)\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020039 
(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))