Average Error: 6.4 → 2.5
Time: 11.8s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.787894993161125728768722537808069209109 \cdot 10^{-291} \lor \neg \left(z \le 4.795758021695445425318685784425559692173 \cdot 10^{-235}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.787894993161125728768722537808069209109 \cdot 10^{-291} \lor \neg \left(z \le 4.795758021695445425318685784425559692173 \cdot 10^{-235}\right):\\
\;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r251287 = x;
        double r251288 = y;
        double r251289 = z;
        double r251290 = t;
        double r251291 = r251289 - r251290;
        double r251292 = r251288 * r251291;
        double r251293 = a;
        double r251294 = r251292 / r251293;
        double r251295 = r251287 - r251294;
        return r251295;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r251296 = z;
        double r251297 = -2.7878949931611257e-291;
        bool r251298 = r251296 <= r251297;
        double r251299 = 4.7957580216954454e-235;
        bool r251300 = r251296 <= r251299;
        double r251301 = !r251300;
        bool r251302 = r251298 || r251301;
        double r251303 = x;
        double r251304 = y;
        double r251305 = a;
        double r251306 = r251304 / r251305;
        double r251307 = t;
        double r251308 = r251296 - r251307;
        double r251309 = r251306 * r251308;
        double r251310 = r251303 - r251309;
        double r251311 = r251305 / r251308;
        double r251312 = r251304 / r251311;
        double r251313 = r251303 - r251312;
        double r251314 = r251302 ? r251310 : r251313;
        return r251314;
}

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

Original6.4
Target0.7
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.7878949931611257e-291 or 4.7957580216954454e-235 < z

    1. Initial program 6.6

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

    3. Applied associate-/l*5.6

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

    5. Applied associate-/r/2.3

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

    if -2.7878949931611257e-291 < z < 4.7957580216954454e-235

    1. Initial program 4.3

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

    3. Applied associate-/l*5.1

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.787894993161125728768722537808069209109 \cdot 10^{-291} \lor \neg \left(z \le 4.795758021695445425318685784425559692173 \cdot 10^{-235}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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)))