Average Error: 10.9 → 0.9
Time: 15.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -186062994224651239424:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\ \mathbf{elif}\;y \le 1.296970934114568854164079327463464100023 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -186062994224651239424:\\
\;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\

\mathbf{elif}\;y \le 1.296970934114568854164079327463464100023 \cdot 10^{-94}:\\
\;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r426365 = x;
        double r426366 = y;
        double r426367 = z;
        double r426368 = t;
        double r426369 = r426367 - r426368;
        double r426370 = r426366 * r426369;
        double r426371 = a;
        double r426372 = r426371 - r426368;
        double r426373 = r426370 / r426372;
        double r426374 = r426365 + r426373;
        return r426374;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r426375 = y;
        double r426376 = -1.8606299422465124e+20;
        bool r426377 = r426375 <= r426376;
        double r426378 = z;
        double r426379 = t;
        double r426380 = r426378 - r426379;
        double r426381 = a;
        double r426382 = r426381 - r426379;
        double r426383 = r426375 / r426382;
        double r426384 = r426380 * r426383;
        double r426385 = x;
        double r426386 = r426384 + r426385;
        double r426387 = 1.2969709341145689e-94;
        bool r426388 = r426375 <= r426387;
        double r426389 = r426380 * r426375;
        double r426390 = r426389 / r426382;
        double r426391 = r426385 + r426390;
        double r426392 = r426382 / r426380;
        double r426393 = r426375 / r426392;
        double r426394 = r426385 + r426393;
        double r426395 = r426388 ? r426391 : r426394;
        double r426396 = r426377 ? r426386 : r426395;
        return r426396;
}

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

Original10.9
Target1.3
Herbie0.9
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -1.8606299422465124e+20

    1. Initial program 24.5

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

    3. Applied *-un-lft-identity24.5

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

    4. Applied times-frac0.8

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

    5. Simplified0.8

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

    7. Applied *-un-lft-identity0.8

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

    8. Applied associate-*l*0.8

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

    9. Simplified3.0

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

    if -1.8606299422465124e+20 < y < 1.2969709341145689e-94

    1. Initial program 0.3

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

    3. Applied *-un-lft-identity0.3

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

    4. Applied times-frac2.2

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

    5. Simplified2.2

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

    7. Applied *-un-lft-identity2.2

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

    8. Applied associate-*l*2.2

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

    9. Simplified3.8

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

    11. Applied associate-*r/0.3

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

    if 1.2969709341145689e-94 < y

    1. Initial program 17.8

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

    3. Applied associate-/l*0.4

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -186062994224651239424:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t} + x\\ \mathbf{elif}\;y \le 1.296970934114568854164079327463464100023 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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))))