Average Error: 1.5 → 0.6
Time: 7.4s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.305314767396193330218747505070664723588 \cdot 10^{-32} \lor \neg \left(y \le 3.568984011627691222092762646146063289201 \cdot 10^{-189}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.305314767396193330218747505070664723588 \cdot 10^{-32} \lor \neg \left(y \le 3.568984011627691222092762646146063289201 \cdot 10^{-189}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{a - 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 r649542 = x;
        double r649543 = y;
        double r649544 = z;
        double r649545 = t;
        double r649546 = r649544 - r649545;
        double r649547 = a;
        double r649548 = r649547 - r649545;
        double r649549 = r649546 / r649548;
        double r649550 = r649543 * r649549;
        double r649551 = r649542 + r649550;
        return r649551;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r649552 = y;
        double r649553 = -4.3053147673961933e-32;
        bool r649554 = r649552 <= r649553;
        double r649555 = 3.5689840116276912e-189;
        bool r649556 = r649552 <= r649555;
        double r649557 = !r649556;
        bool r649558 = r649554 || r649557;
        double r649559 = x;
        double r649560 = z;
        double r649561 = t;
        double r649562 = r649560 - r649561;
        double r649563 = a;
        double r649564 = r649563 - r649561;
        double r649565 = r649562 / r649564;
        double r649566 = r649552 * r649565;
        double r649567 = r649559 + r649566;
        double r649568 = r649552 * r649562;
        double r649569 = r649568 / r649564;
        double r649570 = r649559 + r649569;
        double r649571 = r649558 ? r649567 : r649570;
        return r649571;
}

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

Original1.5
Target0.4
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241069024247453646278348229 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.3053147673961933e-32 or 3.5689840116276912e-189 < y

    1. Initial program 0.9

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

    if -4.3053147673961933e-32 < y < 3.5689840116276912e-189

    1. Initial program 2.8

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

    3. Applied associate-*r/0.2

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.305314767396193330218747505070664723588 \cdot 10^{-32} \lor \neg \left(y \le 3.568984011627691222092762646146063289201 \cdot 10^{-189}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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 -8.50808486055124107e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.8944268627920891e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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