Average Error: 11.3 → 0.5
Time: 4.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -901067.937205575406551361083984375 \lor \neg \left(y \le 5.163724188916300428001985018951606340548 \cdot 10^{-43}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -901067.937205575406551361083984375 \lor \neg \left(y \le 5.163724188916300428001985018951606340548 \cdot 10^{-43}\right):\\
\;\;\;\;x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r572192 = x;
        double r572193 = y;
        double r572194 = z;
        double r572195 = t;
        double r572196 = r572194 - r572195;
        double r572197 = r572193 * r572196;
        double r572198 = a;
        double r572199 = r572194 - r572198;
        double r572200 = r572197 / r572199;
        double r572201 = r572192 + r572200;
        return r572201;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r572202 = y;
        double r572203 = -901067.9372055754;
        bool r572204 = r572202 <= r572203;
        double r572205 = 5.1637241889163004e-43;
        bool r572206 = r572202 <= r572205;
        double r572207 = !r572206;
        bool r572208 = r572204 || r572207;
        double r572209 = x;
        double r572210 = z;
        double r572211 = t;
        double r572212 = r572210 - r572211;
        double r572213 = r572210 / r572212;
        double r572214 = a;
        double r572215 = r572214 / r572212;
        double r572216 = r572213 - r572215;
        double r572217 = r572202 / r572216;
        double r572218 = r572209 + r572217;
        double r572219 = r572202 * r572212;
        double r572220 = r572210 - r572214;
        double r572221 = r572219 / r572220;
        double r572222 = r572209 + r572221;
        double r572223 = r572208 ? r572218 : r572222;
        return r572223;
}

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

Original11.3
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -901067.9372055754 or 5.1637241889163004e-43 < y

    1. Initial program 22.7

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

    3. Applied associate-/l*0.6

      \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
    4. Using strategy rm

    5. Applied div-sub0.6

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

    if -901067.9372055754 < y < 5.1637241889163004e-43

    1. Initial program 0.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -901067.937205575406551361083984375 \lor \neg \left(y \le 5.163724188916300428001985018951606340548 \cdot 10^{-43}\right):\\ \;\;\;\;x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020002 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

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