Average Error: 10.7 → 0.5
Time: 3.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -29005.3023392045252:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;y \le 1.6173790047814861 \cdot 10^{38}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -29005.3023392045252:\\
\;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\

\mathbf{elif}\;y \le 1.6173790047814861 \cdot 10^{38}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r584330 = x;
        double r584331 = y;
        double r584332 = z;
        double r584333 = t;
        double r584334 = r584332 - r584333;
        double r584335 = r584331 * r584334;
        double r584336 = a;
        double r584337 = r584332 - r584336;
        double r584338 = r584335 / r584337;
        double r584339 = r584330 + r584338;
        return r584339;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r584340 = y;
        double r584341 = -29005.302339204525;
        bool r584342 = r584340 <= r584341;
        double r584343 = x;
        double r584344 = z;
        double r584345 = a;
        double r584346 = r584344 - r584345;
        double r584347 = t;
        double r584348 = r584344 - r584347;
        double r584349 = r584346 / r584348;
        double r584350 = r584340 / r584349;
        double r584351 = r584343 + r584350;
        double r584352 = 1.617379004781486e+38;
        bool r584353 = r584340 <= r584352;
        double r584354 = r584340 * r584348;
        double r584355 = r584354 / r584346;
        double r584356 = r584343 + r584355;
        double r584357 = r584348 / r584346;
        double r584358 = r584340 * r584357;
        double r584359 = r584343 + r584358;
        double r584360 = r584353 ? r584356 : r584359;
        double r584361 = r584342 ? r584351 : r584360;
        return r584361;
}

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

Original10.7
Target1.2
Herbie0.5
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -29005.302339204525

    1. Initial program 22.8

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

    3. Applied associate-/l*0.7

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

    if -29005.302339204525 < y < 1.617379004781486e+38

    1. Initial program 0.3

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

    if 1.617379004781486e+38 < y

    1. Initial program 26.5

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

    3. Applied *-un-lft-identity26.5

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

    4. Applied times-frac0.6

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

    5. Simplified0.6

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -29005.3023392045252:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{elif}\;y \le 1.6173790047814861 \cdot 10^{38}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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