Average Error: 1.3 → 0.3
Time: 12.8s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.637379201468953986949485320636358182223 \cdot 10^{-36} \lor \neg \left(y \le 3.205739178188263417782161531329637455788 \cdot 10^{-56}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.637379201468953986949485320636358182223 \cdot 10^{-36} \lor \neg \left(y \le 3.205739178188263417782161531329637455788 \cdot 10^{-56}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{a - t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r399495 = x;
        double r399496 = y;
        double r399497 = z;
        double r399498 = t;
        double r399499 = r399497 - r399498;
        double r399500 = a;
        double r399501 = r399500 - r399498;
        double r399502 = r399499 / r399501;
        double r399503 = r399496 * r399502;
        double r399504 = r399495 + r399503;
        return r399504;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r399505 = y;
        double r399506 = -4.637379201468954e-36;
        bool r399507 = r399505 <= r399506;
        double r399508 = 3.2057391781882634e-56;
        bool r399509 = r399505 <= r399508;
        double r399510 = !r399509;
        bool r399511 = r399507 || r399510;
        double r399512 = x;
        double r399513 = z;
        double r399514 = t;
        double r399515 = r399513 - r399514;
        double r399516 = a;
        double r399517 = r399516 - r399514;
        double r399518 = r399515 / r399517;
        double r399519 = r399505 * r399518;
        double r399520 = r399512 + r399519;
        double r399521 = r399505 * r399515;
        double r399522 = 1.0;
        double r399523 = r399522 / r399517;
        double r399524 = r399521 * r399523;
        double r399525 = r399512 + r399524;
        double r399526 = r399511 ? r399520 : r399525;
        return r399526;
}

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

Original1.3
Target0.3
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.637379201468954e-36 or 3.2057391781882634e-56 < y

    1. Initial program 0.4

      \[x + y \cdot \frac{z - t}{a - t}\]

    if -4.637379201468954e-36 < y < 3.2057391781882634e-56

    1. Initial program 2.3

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

    3. Applied div-inv2.3

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

    4. Applied associate-*r*0.3

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.637379201468953986949485320636358182223 \cdot 10^{-36} \lor \neg \left(y \le 3.205739178188263417782161531329637455788 \cdot 10^{-56}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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