Average Error: 6.2 → 2.6
Time: 9.1s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.3249082459376733 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \le 6.9390753974297484 \cdot 10^{-149}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.3249082459376733 \cdot 10^{-158}:\\
\;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\

\mathbf{elif}\;z \le 6.9390753974297484 \cdot 10^{-149}:\\
\;\;\;\;x + y \cdot \frac{t - z}{a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r395543 = x;
        double r395544 = y;
        double r395545 = z;
        double r395546 = t;
        double r395547 = r395545 - r395546;
        double r395548 = r395544 * r395547;
        double r395549 = a;
        double r395550 = r395548 / r395549;
        double r395551 = r395543 - r395550;
        return r395551;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r395552 = z;
        double r395553 = -5.324908245937673e-158;
        bool r395554 = r395552 <= r395553;
        double r395555 = x;
        double r395556 = y;
        double r395557 = a;
        double r395558 = r395556 / r395557;
        double r395559 = t;
        double r395560 = r395559 - r395552;
        double r395561 = r395558 * r395560;
        double r395562 = r395555 + r395561;
        double r395563 = 6.939075397429748e-149;
        bool r395564 = r395552 <= r395563;
        double r395565 = r395560 / r395557;
        double r395566 = r395556 * r395565;
        double r395567 = r395555 + r395566;
        double r395568 = r395552 - r395559;
        double r395569 = r395557 / r395556;
        double r395570 = r395568 / r395569;
        double r395571 = r395555 - r395570;
        double r395572 = r395564 ? r395567 : r395571;
        double r395573 = r395554 ? r395562 : r395572;
        return r395573;
}

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

Original6.2
Target0.7
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -5.324908245937673e-158

    1. Initial program 7.3

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

    3. Applied sub-neg7.3

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

    4. Simplified2.1

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

    if -5.324908245937673e-158 < z < 6.939075397429748e-149

    1. Initial program 4.2

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

    3. Applied sub-neg4.2

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

    4. Simplified3.5

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

    6. Applied div-inv3.6

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

    7. Applied associate-*l*3.7

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

    8. Simplified3.7

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

    if 6.939075397429748e-149 < z

    1. Initial program 6.5

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

    3. Applied *-un-lft-identity6.5

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

    4. Applied *-un-lft-identity6.5

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

    5. Applied distribute-lft-out--6.5

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

    6. Simplified2.2

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.3249082459376733 \cdot 10^{-158}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \le 6.9390753974297484 \cdot 10^{-149}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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)))