Average Error: 6.1 → 1.3
Time: 4.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.52725015146069365 \cdot 10^{103}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \le 3.7290892044176289 \cdot 10^{-146}:\\ \;\;\;\;x + \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;y \le 2.39946692051228959 \cdot 10^{89}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.52725015146069365 \cdot 10^{103}:\\
\;\;\;\;x + y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;y \le 3.7290892044176289 \cdot 10^{-146}:\\
\;\;\;\;x + \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\

\mathbf{elif}\;y \le 2.39946692051228959 \cdot 10^{89}:\\
\;\;\;\;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 r286974 = x;
        double r286975 = y;
        double r286976 = z;
        double r286977 = t;
        double r286978 = r286976 - r286977;
        double r286979 = r286975 * r286978;
        double r286980 = a;
        double r286981 = r286979 / r286980;
        double r286982 = r286974 + r286981;
        return r286982;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r286983 = y;
        double r286984 = -3.5272501514606936e+103;
        bool r286985 = r286983 <= r286984;
        double r286986 = x;
        double r286987 = z;
        double r286988 = t;
        double r286989 = r286987 - r286988;
        double r286990 = a;
        double r286991 = r286989 / r286990;
        double r286992 = r286983 * r286991;
        double r286993 = r286986 + r286992;
        double r286994 = 3.729089204417629e-146;
        bool r286995 = r286983 <= r286994;
        double r286996 = r286983 * r286987;
        double r286997 = -r286988;
        double r286998 = r286983 * r286997;
        double r286999 = r286996 + r286998;
        double r287000 = r286999 / r286990;
        double r287001 = r286986 + r287000;
        double r287002 = 2.3994669205122896e+89;
        bool r287003 = r286983 <= r287002;
        double r287004 = r286983 / r286990;
        double r287005 = r287004 * r286989;
        double r287006 = r286986 + r287005;
        double r287007 = r286990 / r286989;
        double r287008 = r286983 / r287007;
        double r287009 = r286986 + r287008;
        double r287010 = r287003 ? r287006 : r287009;
        double r287011 = r286995 ? r287001 : r287010;
        double r287012 = r286985 ? r286993 : r287011;
        return r287012;
}

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
Target0.7
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if y < -3.5272501514606936e+103

    1. Initial program 21.8

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

    3. Applied *-un-lft-identity21.8

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

    4. Applied times-frac1.4

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

    5. Simplified1.4

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

    if -3.5272501514606936e+103 < y < 3.729089204417629e-146

    1. Initial program 1.3

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

    3. Applied sub-neg1.3

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

    4. Applied distribute-lft-in1.3

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

    if 3.729089204417629e-146 < y < 2.3994669205122896e+89

    1. Initial program 2.0

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

    3. Applied associate-/l*3.8

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

    5. Applied associate-/r/1.5

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

    if 2.3994669205122896e+89 < y

    1. Initial program 20.3

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

    3. Applied associate-/l*1.3

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.52725015146069365 \cdot 10^{103}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \le 3.7290892044176289 \cdot 10^{-146}:\\ \;\;\;\;x + \frac{y \cdot z + y \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;y \le 2.39946692051228959 \cdot 10^{89}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(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)))