Average Error: 2.1 → 1.8
Time: 15.4s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \le 2.090228760987231008583908788950163454883 \cdot 10^{103}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{y} \le 2.090228760987231008583908788950163454883 \cdot 10^{103}:\\
\;\;\;\;\left(z - t\right) \cdot \frac{x}{y} + t\\

\mathbf{else}:\\
\;\;\;\;t + x \cdot \frac{z - t}{y}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r342587 = x;
        double r342588 = y;
        double r342589 = r342587 / r342588;
        double r342590 = z;
        double r342591 = t;
        double r342592 = r342590 - r342591;
        double r342593 = r342589 * r342592;
        double r342594 = r342593 + r342591;
        return r342594;
}
↓
double f(double x, double y, double z, double t) {
        double r342595 = x;
        double r342596 = y;
        double r342597 = r342595 / r342596;
        double r342598 = 2.090228760987231e+103;
        bool r342599 = r342597 <= r342598;
        double r342600 = z;
        double r342601 = t;
        double r342602 = r342600 - r342601;
        double r342603 = r342602 * r342597;
        double r342604 = r342603 + r342601;
        double r342605 = r342602 / r342596;
        double r342606 = r342595 * r342605;
        double r342607 = r342601 + r342606;
        double r342608 = r342599 ? r342604 : r342607;
        return r342608;
}

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
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ x y) < 2.090228760987231e+103

    1. Initial program 1.5

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

    3. Applied *-commutative1.5

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

    if 2.090228760987231e+103 < (/ x y)

    1. Initial program 8.5

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

    3. Applied div-inv8.6

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

    4. Applied associate-*l*5.5

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

    5. Simplified5.3

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \le 2.090228760987231008583908788950163454883 \cdot 10^{103}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +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))