Average Error: 5.9 → 0.9
Time: 3.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.1473918177297942 \cdot 10^{219}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 6.43849552264531777 \cdot 10^{124}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -1.1473918177297942 \cdot 10^{219}:\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 6.43849552264531777 \cdot 10^{124}:\\
\;\;\;\;x + \frac{1}{\frac{a}{y \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 r301368 = x;
        double r301369 = y;
        double r301370 = z;
        double r301371 = t;
        double r301372 = r301370 - r301371;
        double r301373 = r301369 * r301372;
        double r301374 = a;
        double r301375 = r301373 / r301374;
        double r301376 = r301368 + r301375;
        return r301376;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r301377 = y;
        double r301378 = z;
        double r301379 = t;
        double r301380 = r301378 - r301379;
        double r301381 = r301377 * r301380;
        double r301382 = -1.1473918177297942e+219;
        bool r301383 = r301381 <= r301382;
        double r301384 = x;
        double r301385 = a;
        double r301386 = r301377 / r301385;
        double r301387 = r301386 * r301380;
        double r301388 = r301384 + r301387;
        double r301389 = 6.438495522645318e+124;
        bool r301390 = r301381 <= r301389;
        double r301391 = 1.0;
        double r301392 = r301385 / r301381;
        double r301393 = r301391 / r301392;
        double r301394 = r301384 + r301393;
        double r301395 = r301385 / r301380;
        double r301396 = r301377 / r301395;
        double r301397 = r301384 + r301396;
        double r301398 = r301390 ? r301394 : r301397;
        double r301399 = r301383 ? r301388 : r301398;
        return r301399;
}

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

Original5.9
Target0.7
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -1.1473918177297942e+219

    1. Initial program 30.3

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

    3. Applied associate-/l*0.4

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

    5. Applied associate-/r/0.6

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

    if -1.1473918177297942e+219 < (* y (- z t)) < 6.438495522645318e+124

    1. Initial program 0.5

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

    3. Applied clear-num0.5

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

    if 6.438495522645318e+124 < (* y (- z t))

    1. Initial program 17.6

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

    3. Applied associate-/l*2.6

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.1473918177297942 \cdot 10^{219}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 6.43849552264531777 \cdot 10^{124}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(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)))