Average Error: 1.9 → 2.0
Time: 4.7s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 1.9303930253189972 \cdot 10^{-284} \lor \neg \left(t \le 8.4653916187619271 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} \cdot x + \frac{-t}{y} \cdot x\right) + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le 1.9303930253189972 \cdot 10^{-284} \lor \neg \left(t \le 8.4653916187619271 \cdot 10^{-56}\right):\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r597508 = x;
        double r597509 = y;
        double r597510 = r597508 / r597509;
        double r597511 = z;
        double r597512 = t;
        double r597513 = r597511 - r597512;
        double r597514 = r597510 * r597513;
        double r597515 = r597514 + r597512;
        return r597515;
}
↓
double f(double x, double y, double z, double t) {
        double r597516 = t;
        double r597517 = 1.9303930253189972e-284;
        bool r597518 = r597516 <= r597517;
        double r597519 = 8.465391618761927e-56;
        bool r597520 = r597516 <= r597519;
        double r597521 = !r597520;
        bool r597522 = r597518 || r597521;
        double r597523 = x;
        double r597524 = y;
        double r597525 = r597523 / r597524;
        double r597526 = z;
        double r597527 = r597526 - r597516;
        double r597528 = r597525 * r597527;
        double r597529 = r597528 + r597516;
        double r597530 = r597526 / r597524;
        double r597531 = r597530 * r597523;
        double r597532 = -r597516;
        double r597533 = r597532 / r597524;
        double r597534 = r597533 * r597523;
        double r597535 = r597531 + r597534;
        double r597536 = r597535 + r597516;
        double r597537 = r597522 ? r597529 : r597536;
        return r597537;
}

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

Original1.9
Target2.3
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < 1.9303930253189972e-284 or 8.465391618761927e-56 < t

    1. Initial program 1.5

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

    if 1.9303930253189972e-284 < t < 8.465391618761927e-56

    1. Initial program 3.8

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

    3. Applied *-un-lft-identity3.8

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

    4. Applied add-cube-cbrt4.5

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

    5. Applied times-frac4.5

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

    6. Applied associate-*l*3.5

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

    8. Applied sub-neg3.5

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

    9. Applied distribute-lft-in3.5

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

    10. Applied distribute-lft-in3.5

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

    11. Simplified4.4

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

    12. Simplified4.2

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 1.9303930253189972 \cdot 10^{-284} \lor \neg \left(t \le 8.4653916187619271 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{y} \cdot x + \frac{-t}{y} \cdot x\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 
(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))