Average Error: 6.3 → 1.4
Time: 3.6s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -4.9168923767645714 \cdot 10^{80}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.08730857278766648 \cdot 10^{115}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -4.9168923767645714 \cdot 10^{80}:\\
\;\;\;\;x - y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 2.08730857278766648 \cdot 10^{115}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r353263 = x;
        double r353264 = y;
        double r353265 = z;
        double r353266 = t;
        double r353267 = r353265 - r353266;
        double r353268 = r353264 * r353267;
        double r353269 = a;
        double r353270 = r353268 / r353269;
        double r353271 = r353263 - r353270;
        return r353271;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r353272 = y;
        double r353273 = z;
        double r353274 = t;
        double r353275 = r353273 - r353274;
        double r353276 = r353272 * r353275;
        double r353277 = -4.916892376764571e+80;
        bool r353278 = r353276 <= r353277;
        double r353279 = x;
        double r353280 = a;
        double r353281 = r353275 / r353280;
        double r353282 = r353272 * r353281;
        double r353283 = r353279 - r353282;
        double r353284 = 2.0873085727876665e+115;
        bool r353285 = r353276 <= r353284;
        double r353286 = r353276 / r353280;
        double r353287 = r353279 - r353286;
        double r353288 = r353272 / r353280;
        double r353289 = r353288 * r353275;
        double r353290 = r353279 - r353289;
        double r353291 = r353285 ? r353287 : r353290;
        double r353292 = r353278 ? r353283 : r353291;
        return r353292;
}

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

Original6.3
Target0.7
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -4.916892376764571e+80

    1. Initial program 14.6

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

    3. Applied *-un-lft-identity14.6

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

    4. Applied times-frac3.8

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

    5. Simplified3.8

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

    if -4.916892376764571e+80 < (* y (- z t)) < 2.0873085727876665e+115

    1. Initial program 0.5

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

    if 2.0873085727876665e+115 < (* y (- z t))

    1. Initial program 18.1

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

    3. Applied associate-/l*2.7

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

    5. Applied associate-/r/2.2

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -4.9168923767645714 \cdot 10^{80}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.08730857278766648 \cdot 10^{115}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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