Average Error: 6.3 → 1.4
Time: 3.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -4.9168923767645714 \cdot 10^{80}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.08730857278766648 \cdot 10^{115}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \end{array}\]
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 + \frac{y}{\frac{a}{z - t}}\\

\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 r424307 = x;
        double r424308 = y;
        double r424309 = z;
        double r424310 = t;
        double r424311 = r424309 - r424310;
        double r424312 = r424308 * r424311;
        double r424313 = a;
        double r424314 = r424312 / r424313;
        double r424315 = r424307 + r424314;
        return r424315;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r424316 = y;
        double r424317 = z;
        double r424318 = t;
        double r424319 = r424317 - r424318;
        double r424320 = r424316 * r424319;
        double r424321 = -4.916892376764571e+80;
        bool r424322 = r424320 <= r424321;
        double r424323 = x;
        double r424324 = a;
        double r424325 = r424324 / r424319;
        double r424326 = r424316 / r424325;
        double r424327 = r424323 + r424326;
        double r424328 = 2.0873085727876665e+115;
        bool r424329 = r424320 <= r424328;
        double r424330 = r424320 / r424324;
        double r424331 = r424323 + r424330;
        double r424332 = r424316 / r424324;
        double r424333 = r424332 * r424319;
        double r424334 = r424323 + r424333;
        double r424335 = r424329 ? r424331 : r424334;
        double r424336 = r424322 ? r424327 : r424335;
        return r424336;
}

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 associate-/l*3.4

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

    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

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

Reproduce

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