Average Error: 6.3 → 1.0
Time: 7.3s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.8638720380733864 \cdot 10^{137} \lor \neg \left(y \cdot \left(z - t\right) \le 1.10810879622775848 \cdot 10^{56}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -1.8638720380733864 \cdot 10^{137} \lor \neg \left(y \cdot \left(z - t\right) \le 1.10810879622775848 \cdot 10^{56}\right):\\
\;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r196223 = x;
        double r196224 = y;
        double r196225 = z;
        double r196226 = t;
        double r196227 = r196225 - r196226;
        double r196228 = r196224 * r196227;
        double r196229 = a;
        double r196230 = r196228 / r196229;
        double r196231 = r196223 + r196230;
        return r196231;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r196232 = y;
        double r196233 = z;
        double r196234 = t;
        double r196235 = r196233 - r196234;
        double r196236 = r196232 * r196235;
        double r196237 = -1.8638720380733864e+137;
        bool r196238 = r196236 <= r196237;
        double r196239 = 1.1081087962277585e+56;
        bool r196240 = r196236 <= r196239;
        double r196241 = !r196240;
        bool r196242 = r196238 || r196241;
        double r196243 = x;
        double r196244 = a;
        double r196245 = r196244 / r196232;
        double r196246 = r196235 / r196245;
        double r196247 = r196243 + r196246;
        double r196248 = r196236 / r196244;
        double r196249 = r196243 + r196248;
        double r196250 = r196242 ? r196247 : r196249;
        return r196250;
}

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
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -1.8638720380733864e+137 or 1.1081087962277585e+56 < (* y (- z t))

    1. Initial program 16.1

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

    3. Applied associate-/l*3.2

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

    5. Applied associate-/r/1.9

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

    7. Applied pow11.9

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

    8. Applied pow11.9

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

    9. Applied pow-prod-down1.9

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

    10. Simplified1.9

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

    if -1.8638720380733864e+137 < (* y (- z t)) < 1.1081087962277585e+56

    1. Initial program 0.5

      \[x + \frac{y \cdot \left(z - t\right)}{a}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.8638720380733864 \cdot 10^{137} \lor \neg \left(y \cdot \left(z - t\right) \le 1.10810879622775848 \cdot 10^{56}\right):\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))