Average Error: 10.7 → 1.0
Time: 4.9s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \le -2.71996673673692891 \cdot 10^{103} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 8.4283542794731453 \cdot 10^{197}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \le -2.71996673673692891 \cdot 10^{103} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 8.4283542794731453 \cdot 10^{197}\right):\\
\;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r702227 = x;
        double r702228 = y;
        double r702229 = z;
        double r702230 = r702228 - r702229;
        double r702231 = t;
        double r702232 = r702230 * r702231;
        double r702233 = a;
        double r702234 = r702233 - r702229;
        double r702235 = r702232 / r702234;
        double r702236 = r702227 + r702235;
        return r702236;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r702237 = y;
        double r702238 = z;
        double r702239 = r702237 - r702238;
        double r702240 = t;
        double r702241 = r702239 * r702240;
        double r702242 = a;
        double r702243 = r702242 - r702238;
        double r702244 = r702241 / r702243;
        double r702245 = -2.719966736736929e+103;
        bool r702246 = r702244 <= r702245;
        double r702247 = 8.428354279473145e+197;
        bool r702248 = r702244 <= r702247;
        double r702249 = !r702248;
        bool r702250 = r702246 || r702249;
        double r702251 = x;
        double r702252 = r702243 / r702240;
        double r702253 = r702239 / r702252;
        double r702254 = r702251 + r702253;
        double r702255 = r702251 + r702244;
        double r702256 = r702250 ? r702254 : r702255;
        return r702256;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.7
Target0.6
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (- y z) t) (- a z)) < -2.719966736736929e+103 or 8.428354279473145e+197 < (/ (* (- y z) t) (- a z))

    1. Initial program 38.9

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

    3. Applied associate-/l*3.0

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

    if -2.719966736736929e+103 < (/ (* (- y z) t) (- a z)) < 8.428354279473145e+197

    1. Initial program 0.3

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \le -2.71996673673692891 \cdot 10^{103} \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 8.4283542794731453 \cdot 10^{197}\right):\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020034 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

  (+ x (/ (* (- y z) t) (- a z))))