Average Error: 6.0 → 0.5
Time: 11.4s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.16469840953694673 \cdot 10^{185}:\\ \;\;\;\;x - \frac{z - t}{a} \cdot y\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.424193312752178 \cdot 10^{192}:\\ \;\;\;\;x - \left(\frac{z \cdot y}{a} - \frac{t \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -1.16469840953694673 \cdot 10^{185}:\\
\;\;\;\;x - \frac{z - t}{a} \cdot y\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 2.424193312752178 \cdot 10^{192}:\\
\;\;\;\;x - \left(\frac{z \cdot y}{a} - \frac{t \cdot y}{a}\right)\\

\mathbf{else}:\\
\;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r368488 = x;
        double r368489 = y;
        double r368490 = z;
        double r368491 = t;
        double r368492 = r368490 - r368491;
        double r368493 = r368489 * r368492;
        double r368494 = a;
        double r368495 = r368493 / r368494;
        double r368496 = r368488 - r368495;
        return r368496;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r368497 = y;
        double r368498 = z;
        double r368499 = t;
        double r368500 = r368498 - r368499;
        double r368501 = r368497 * r368500;
        double r368502 = -1.1646984095369467e+185;
        bool r368503 = r368501 <= r368502;
        double r368504 = x;
        double r368505 = a;
        double r368506 = r368500 / r368505;
        double r368507 = r368506 * r368497;
        double r368508 = r368504 - r368507;
        double r368509 = 2.424193312752178e+192;
        bool r368510 = r368501 <= r368509;
        double r368511 = r368498 * r368497;
        double r368512 = r368511 / r368505;
        double r368513 = r368499 * r368497;
        double r368514 = r368513 / r368505;
        double r368515 = r368512 - r368514;
        double r368516 = r368504 - r368515;
        double r368517 = r368505 / r368497;
        double r368518 = r368500 / r368517;
        double r368519 = r368504 - r368518;
        double r368520 = r368510 ? r368516 : r368519;
        double r368521 = r368503 ? r368508 : r368520;
        return r368521;
}

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

Original6.0
Target0.6
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -1.1646984095369467e+185

    1. Initial program 24.7

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

    3. Applied *-un-lft-identity24.7

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

    4. Applied *-un-lft-identity24.7

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

    5. Applied distribute-lft-out--24.7

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

    6. Simplified0.7

      \[\leadsto 1 \cdot \color{blue}{\left(x - \frac{z - t}{\frac{a}{y}}\right)}\]
    7. Using strategy rm

    8. Applied associate-/r/1.3

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

    if -1.1646984095369467e+185 < (* y (- z t)) < 2.424193312752178e+192

    1. Initial program 0.4

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

    3. Applied *-un-lft-identity0.4

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

    4. Applied *-un-lft-identity0.4

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

    5. Applied distribute-lft-out--0.4

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

    6. Simplified3.1

      \[\leadsto 1 \cdot \color{blue}{\left(x - \frac{z - t}{\frac{a}{y}}\right)}\]
    7. Using strategy rm

    8. Applied div-sub3.1

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

    9. Simplified2.6

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

    10. Simplified0.4

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

    if 2.424193312752178e+192 < (* y (- z t))

    1. Initial program 26.2

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

    3. Applied *-un-lft-identity26.2

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

    4. Applied *-un-lft-identity26.2

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

    5. Applied distribute-lft-out--26.2

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

    6. Simplified1.0

      \[\leadsto 1 \cdot \color{blue}{\left(x - \frac{z - t}{\frac{a}{y}}\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -1.16469840953694673 \cdot 10^{185}:\\ \;\;\;\;x - \frac{z - t}{a} \cdot y\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.424193312752178 \cdot 10^{192}:\\ \;\;\;\;x - \left(\frac{z \cdot y}{a} - \frac{t \cdot y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :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)))