Average Error: 1.3 → 0.4
Time: 16.6s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.278223167257424843811284870496496436881 \cdot 10^{-23}:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y + x\\ \mathbf{elif}\;y \le 4.106049947800754326326111224585926281167 \cdot 10^{-80}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y + x\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.278223167257424843811284870496496436881 \cdot 10^{-23}:\\
\;\;\;\;\frac{z - t}{a - t} \cdot y + x\\

\mathbf{elif}\;y \le 4.106049947800754326326111224585926281167 \cdot 10^{-80}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r27541363 = x;
        double r27541364 = y;
        double r27541365 = z;
        double r27541366 = t;
        double r27541367 = r27541365 - r27541366;
        double r27541368 = a;
        double r27541369 = r27541368 - r27541366;
        double r27541370 = r27541367 / r27541369;
        double r27541371 = r27541364 * r27541370;
        double r27541372 = r27541363 + r27541371;
        return r27541372;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r27541373 = y;
        double r27541374 = -2.2782231672574248e-23;
        bool r27541375 = r27541373 <= r27541374;
        double r27541376 = z;
        double r27541377 = t;
        double r27541378 = r27541376 - r27541377;
        double r27541379 = a;
        double r27541380 = r27541379 - r27541377;
        double r27541381 = r27541378 / r27541380;
        double r27541382 = r27541381 * r27541373;
        double r27541383 = x;
        double r27541384 = r27541382 + r27541383;
        double r27541385 = 4.106049947800754e-80;
        bool r27541386 = r27541373 <= r27541385;
        double r27541387 = r27541373 * r27541378;
        double r27541388 = 1.0;
        double r27541389 = r27541388 / r27541380;
        double r27541390 = r27541387 * r27541389;
        double r27541391 = r27541383 + r27541390;
        double r27541392 = r27541386 ? r27541391 : r27541384;
        double r27541393 = r27541375 ? r27541384 : r27541392;
        return r27541393;
}

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

Derivation

  1. Split input into 2 regimes

  2. if y < -2.2782231672574248e-23 or 4.106049947800754e-80 < y

    1. Initial program 0.4

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

    if -2.2782231672574248e-23 < y < 4.106049947800754e-80

    1. Initial program 2.5

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

    3. Applied div-inv2.5

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

    4. Applied associate-*r*0.5

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.278223167257424843811284870496496436881 \cdot 10^{-23}:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y + x\\ \mathbf{elif}\;y \le 4.106049947800754326326111224585926281167 \cdot 10^{-80}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{a - t} \cdot y + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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