Average Error: 6.1 → 0.5
Time: 18.3s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \le -5.843678163410402 \cdot 10^{+199}:\\ \;\;\;\;x - \frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;\left(z - t\right) \cdot y \le 3.7199348004809193 \cdot 10^{+172}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(\frac{z}{a} - \frac{t}{a}\right)\\ \end{array}\]
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{z}{a} - \frac{t}{a}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r19459659 = x;
        double r19459660 = y;
        double r19459661 = z;
        double r19459662 = t;
        double r19459663 = r19459661 - r19459662;
        double r19459664 = r19459660 * r19459663;
        double r19459665 = a;
        double r19459666 = r19459664 / r19459665;
        double r19459667 = r19459659 - r19459666;
        return r19459667;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r19459668 = z;
        double r19459669 = t;
        double r19459670 = r19459668 - r19459669;
        double r19459671 = y;
        double r19459672 = r19459670 * r19459671;
        double r19459673 = -5.843678163410402e+199;
        bool r19459674 = r19459672 <= r19459673;
        double r19459675 = x;
        double r19459676 = a;
        double r19459677 = r19459676 / r19459671;
        double r19459678 = r19459670 / r19459677;
        double r19459679 = r19459675 - r19459678;
        double r19459680 = 3.7199348004809193e+172;
        bool r19459681 = r19459672 <= r19459680;
        double r19459682 = r19459672 / r19459676;
        double r19459683 = r19459675 - r19459682;
        double r19459684 = r19459668 / r19459676;
        double r19459685 = r19459669 / r19459676;
        double r19459686 = r19459684 - r19459685;
        double r19459687 = r19459671 * r19459686;
        double r19459688 = r19459675 - r19459687;
        double r19459689 = r19459681 ? r19459683 : r19459688;
        double r19459690 = r19459674 ? r19459679 : r19459689;
        return r19459690;
}

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. Using strategy rm

    3. Applied add-cube-cbrt23.7

      \[\leadsto x - \frac{y \cdot \left(z - t\right)}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}\]

    4. Applied times-frac1.7

      \[\leadsto x - \color{blue}{\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}}\]

    5. Taylor expanded around 0 23.2

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

    6. Simplified1.4

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

  4. Final simplification0.5

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

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)))