Average Error: 1.3 → 0.6
Time: 4.8s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.1226440860784546 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{z - a}\right)\\ \mathbf{elif}\;y \le 1.8327693131812995 \cdot 10^{27}:\\ \;\;\;\;x + \left(\left(z - t\right) \cdot y\right) \cdot \frac{1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{1}{\frac{z - a}{z - t}}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.1226440860784546 \cdot 10^{-64}:\\
\;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{z - a}\right)\\

\mathbf{elif}\;y \le 1.8327693131812995 \cdot 10^{27}:\\
\;\;\;\;x + \left(\left(z - t\right) \cdot y\right) \cdot \frac{1}{z - a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r543329 = x;
        double r543330 = y;
        double r543331 = z;
        double r543332 = t;
        double r543333 = r543331 - r543332;
        double r543334 = a;
        double r543335 = r543331 - r543334;
        double r543336 = r543333 / r543335;
        double r543337 = r543330 * r543336;
        double r543338 = r543329 + r543337;
        return r543338;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r543339 = y;
        double r543340 = -1.1226440860784546e-64;
        bool r543341 = r543339 <= r543340;
        double r543342 = x;
        double r543343 = z;
        double r543344 = t;
        double r543345 = r543343 - r543344;
        double r543346 = 1.0;
        double r543347 = a;
        double r543348 = r543343 - r543347;
        double r543349 = r543346 / r543348;
        double r543350 = r543345 * r543349;
        double r543351 = r543339 * r543350;
        double r543352 = r543342 + r543351;
        double r543353 = 1.8327693131812995e+27;
        bool r543354 = r543339 <= r543353;
        double r543355 = r543345 * r543339;
        double r543356 = r543355 * r543349;
        double r543357 = r543342 + r543356;
        double r543358 = r543348 / r543345;
        double r543359 = r543346 / r543358;
        double r543360 = r543339 * r543359;
        double r543361 = r543342 + r543360;
        double r543362 = r543354 ? r543357 : r543361;
        double r543363 = r543341 ? r543352 : r543362;
        return r543363;
}

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
Target1.2
Herbie0.6
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.1226440860784546e-64

    1. Initial program 0.7

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

    3. Applied div-inv0.8

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

    if -1.1226440860784546e-64 < y < 1.8327693131812995e+27

    1. Initial program 2.1

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

    3. Applied div-inv2.1

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

    5. Applied associate-*r*0.5

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

    6. Simplified0.5

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

    if 1.8327693131812995e+27 < y

    1. Initial program 0.5

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

    3. Applied clear-num0.6

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.1226440860784546 \cdot 10^{-64}:\\ \;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{z - a}\right)\\ \mathbf{elif}\;y \le 1.8327693131812995 \cdot 10^{27}:\\ \;\;\;\;x + \left(\left(z - t\right) \cdot y\right) \cdot \frac{1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{1}{\frac{z - a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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