Average Error: 6.1 → 0.5
Time: 3.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 2.995469952665014041540810221972499392166 \cdot 10^{202}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 2.995469952665014041540810221972499392166 \cdot 10^{202}\right):\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

\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 r346598 = x;
        double r346599 = y;
        double r346600 = z;
        double r346601 = t;
        double r346602 = r346600 - r346601;
        double r346603 = r346599 * r346602;
        double r346604 = a;
        double r346605 = r346603 / r346604;
        double r346606 = r346598 + r346605;
        return r346606;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r346607 = y;
        double r346608 = z;
        double r346609 = t;
        double r346610 = r346608 - r346609;
        double r346611 = r346607 * r346610;
        double r346612 = -inf.0;
        bool r346613 = r346611 <= r346612;
        double r346614 = 2.995469952665014e+202;
        bool r346615 = r346611 <= r346614;
        double r346616 = !r346615;
        bool r346617 = r346613 || r346616;
        double r346618 = x;
        double r346619 = a;
        double r346620 = r346607 / r346619;
        double r346621 = r346620 * r346610;
        double r346622 = r346618 + r346621;
        double r346623 = r346611 / r346619;
        double r346624 = r346618 + r346623;
        double r346625 = r346617 ? r346622 : r346624;
        return r346625;
}

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

Original6.1
Target0.8
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -inf.0 or 2.995469952665014e+202 < (* y (- z t))

    1. Initial program 39.5

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

    3. Applied associate-/l*0.6

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

    5. Applied associate-/r/0.6

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

    if -inf.0 < (* y (- z t)) < 2.995469952665014e+202

    1. Initial program 0.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 2.995469952665014041540810221972499392166 \cdot 10^{202}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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)))