Average Error: 1.8 → 1.2
Time: 4.3s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \le 9.22723325612302708 \cdot 10^{244}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;\frac{x}{y} \le 9.22723325612302708 \cdot 10^{244}:\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r428698 = x;
        double r428699 = y;
        double r428700 = r428698 / r428699;
        double r428701 = z;
        double r428702 = t;
        double r428703 = r428701 - r428702;
        double r428704 = r428700 * r428703;
        double r428705 = r428704 + r428702;
        return r428705;
}
↓
double f(double x, double y, double z, double t) {
        double r428706 = x;
        double r428707 = y;
        double r428708 = r428706 / r428707;
        double r428709 = 9.227233256123027e+244;
        bool r428710 = r428708 <= r428709;
        double r428711 = z;
        double r428712 = t;
        double r428713 = r428711 - r428712;
        double r428714 = r428708 * r428713;
        double r428715 = r428714 + r428712;
        double r428716 = r428706 * r428713;
        double r428717 = r428716 / r428707;
        double r428718 = r428717 + r428712;
        double r428719 = r428710 ? r428715 : r428718;
        return r428719;
}

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

Original1.8
Target2.0
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ x y) < 9.227233256123027e+244

    1. Initial program 1.2

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

    if 9.227233256123027e+244 < (/ x y)

    1. Initial program 29.2

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

    3. Applied associate-*l/0.9

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \le 9.22723325612302708 \cdot 10^{244}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(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))