Average Error: 2.1 → 1.8
Time: 14.3s
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 r660162 = x;
        double r660163 = y;
        double r660164 = r660162 / r660163;
        double r660165 = z;
        double r660166 = t;
        double r660167 = r660165 - r660166;
        double r660168 = r660164 * r660167;
        double r660169 = r660168 + r660166;
        return r660169;
}
↓
double f(double x, double y, double z, double t) {
        double r660170 = x;
        double r660171 = y;
        double r660172 = r660170 / r660171;
        double r660173 = 2.090228760987231e+103;
        bool r660174 = r660172 <= r660173;
        double r660175 = z;
        double r660176 = t;
        double r660177 = r660175 - r660176;
        double r660178 = r660177 * r660172;
        double r660179 = r660178 + r660176;
        double r660180 = r660177 / r660171;
        double r660181 = r660170 * r660180;
        double r660182 = r660176 + r660181;
        double r660183 = r660174 ? r660179 : r660182;
        return r660183;
}

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

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

    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 
(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))