Average Error: 10.7 → 0.5
Time: 2.9s
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 r677258 = x;
        double r677259 = y;
        double r677260 = z;
        double r677261 = t;
        double r677262 = r677260 - r677261;
        double r677263 = r677259 * r677262;
        double r677264 = a;
        double r677265 = r677260 - r677264;
        double r677266 = r677263 / r677265;
        double r677267 = r677258 + r677266;
        return r677267;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r677268 = y;
        double r677269 = -29005.302339204525;
        bool r677270 = r677268 <= r677269;
        double r677271 = x;
        double r677272 = z;
        double r677273 = a;
        double r677274 = r677272 - r677273;
        double r677275 = t;
        double r677276 = r677272 - r677275;
        double r677277 = r677274 / r677276;
        double r677278 = r677268 / r677277;
        double r677279 = r677271 + r677278;
        double r677280 = 1.617379004781486e+38;
        bool r677281 = r677268 <= r677280;
        double r677282 = r677268 * r677276;
        double r677283 = r677282 / r677274;
        double r677284 = r677271 + r677283;
        double r677285 = r677276 / r677274;
        double r677286 = r677268 * r677285;
        double r677287 = r677271 + r677286;
        double r677288 = r677281 ? r677284 : r677287;
        double r677289 = r677270 ? r677279 : r677288;
        return r677289;
}

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 
(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))))