Average Error: 11.5 → 0.7
Time: 5.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -6.414154112854105407013291321620742388699 \cdot 10^{-121} \lor \neg \left(y \le 4.594501379393755892248903622673783295757 \cdot 10^{-163}\right):\\ \;\;\;\;x + \frac{y}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -6.414154112854105407013291321620742388699 \cdot 10^{-121} \lor \neg \left(y \le 4.594501379393755892248903622673783295757 \cdot 10^{-163}\right):\\
\;\;\;\;x + \frac{y}{\left(a - t\right) \cdot \frac{1}{z - t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r651419 = x;
        double r651420 = y;
        double r651421 = z;
        double r651422 = t;
        double r651423 = r651421 - r651422;
        double r651424 = r651420 * r651423;
        double r651425 = a;
        double r651426 = r651425 - r651422;
        double r651427 = r651424 / r651426;
        double r651428 = r651419 + r651427;
        return r651428;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r651429 = y;
        double r651430 = -6.414154112854105e-121;
        bool r651431 = r651429 <= r651430;
        double r651432 = 4.594501379393756e-163;
        bool r651433 = r651429 <= r651432;
        double r651434 = !r651433;
        bool r651435 = r651431 || r651434;
        double r651436 = x;
        double r651437 = a;
        double r651438 = t;
        double r651439 = r651437 - r651438;
        double r651440 = 1.0;
        double r651441 = z;
        double r651442 = r651441 - r651438;
        double r651443 = r651440 / r651442;
        double r651444 = r651439 * r651443;
        double r651445 = r651429 / r651444;
        double r651446 = r651436 + r651445;
        double r651447 = r651429 * r651442;
        double r651448 = r651447 / r651439;
        double r651449 = r651436 + r651448;
        double r651450 = r651435 ? r651446 : r651449;
        return r651450;
}

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

Original11.5
Target1.4
Herbie0.7
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -6.414154112854105e-121 or 4.594501379393756e-163 < y

    1. Initial program 16.0

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

    3. Applied associate-/l*0.8

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

    5. Applied div-inv0.9

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

    if -6.414154112854105e-121 < y < 4.594501379393756e-163

    1. Initial program 0.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -6.414154112854105407013291321620742388699 \cdot 10^{-121} \lor \neg \left(y \le 4.594501379393755892248903622673783295757 \cdot 10^{-163}\right):\\ \;\;\;\;x + \frac{y}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019353 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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