Average Error: 6.4 → 2.5
Time: 16.8s
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 r221181 = x;
        double r221182 = y;
        double r221183 = z;
        double r221184 = t;
        double r221185 = r221183 - r221184;
        double r221186 = r221182 * r221185;
        double r221187 = a;
        double r221188 = r221186 / r221187;
        double r221189 = r221181 + r221188;
        return r221189;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r221190 = z;
        double r221191 = -2.7878949931611257e-291;
        bool r221192 = r221190 <= r221191;
        double r221193 = 4.7957580216954454e-235;
        bool r221194 = r221190 <= r221193;
        double r221195 = !r221194;
        bool r221196 = r221192 || r221195;
        double r221197 = x;
        double r221198 = y;
        double r221199 = a;
        double r221200 = r221198 / r221199;
        double r221201 = t;
        double r221202 = r221190 - r221201;
        double r221203 = r221200 * r221202;
        double r221204 = r221197 + r221203;
        double r221205 = r221199 / r221202;
        double r221206 = r221198 / r221205;
        double r221207 = r221197 + r221206;
        double r221208 = r221196 ? r221204 : r221207;
        return r221208;
}

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, E"
  :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)))