Average Error: 6.1 → 0.5
Time: 17.2s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \le -5.843678163410402 \cdot 10^{+199}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;\left(z - t\right) \cdot y \le 3.7199348004809193 \cdot 10^{+172}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{a} - \frac{z}{a}\right)\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;\left(z - t\right) \cdot y \le -5.843678163410402 \cdot 10^{+199}:\\
\;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\

\mathbf{elif}\;\left(z - t\right) \cdot y \le 3.7199348004809193 \cdot 10^{+172}:\\
\;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \left(\frac{t}{a} - \frac{z}{a}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r18109700 = x;
        double r18109701 = y;
        double r18109702 = z;
        double r18109703 = t;
        double r18109704 = r18109702 - r18109703;
        double r18109705 = r18109701 * r18109704;
        double r18109706 = a;
        double r18109707 = r18109705 / r18109706;
        double r18109708 = r18109700 - r18109707;
        return r18109708;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r18109709 = z;
        double r18109710 = t;
        double r18109711 = r18109709 - r18109710;
        double r18109712 = y;
        double r18109713 = r18109711 * r18109712;
        double r18109714 = -5.843678163410402e+199;
        bool r18109715 = r18109713 <= r18109714;
        double r18109716 = x;
        double r18109717 = a;
        double r18109718 = r18109717 / r18109712;
        double r18109719 = r18109711 / r18109718;
        double r18109720 = r18109716 - r18109719;
        double r18109721 = 3.7199348004809193e+172;
        bool r18109722 = r18109713 <= r18109721;
        double r18109723 = r18109713 / r18109717;
        double r18109724 = r18109716 - r18109723;
        double r18109725 = r18109710 / r18109717;
        double r18109726 = r18109709 / r18109717;
        double r18109727 = r18109725 - r18109726;
        double r18109728 = r18109712 * r18109727;
        double r18109729 = r18109716 + r18109728;
        double r18109730 = r18109722 ? r18109724 : r18109729;
        double r18109731 = r18109715 ? r18109720 : r18109730;
        return r18109731;
}

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
Target0.6
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -5.843678163410402e+199

    1. Initial program 29.4

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

    2. Taylor expanded around 0 29.4

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

    3. Simplified0.7

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

    if -5.843678163410402e+199 < (* y (- z t)) < 3.7199348004809193e+172

    1. Initial program 0.4

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

    if 3.7199348004809193e+172 < (* y (- z t))

    1. Initial program 23.2

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

    2. Taylor expanded around 0 23.2

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

    3. Simplified1.0

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

    5. Applied div-inv1.1

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

    6. Simplified0.9

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

    7. Taylor expanded around 0 23.2

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

    8. Simplified1.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \le -5.843678163410402 \cdot 10^{+199}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;\left(z - t\right) \cdot y \le 3.7199348004809193 \cdot 10^{+172}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{a} - \frac{z}{a}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"

  :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)))