Average Error: 6.0 → 0.5
Time: 10.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -3.2688106303761396 \cdot 10^{233}:\\ \;\;\;\;x + \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.8461840642724514 \cdot 10^{164}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -3.2688106303761396 \cdot 10^{233}:\\
\;\;\;\;x + \frac{\frac{y}{a}}{\frac{1}{z - t}}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 2.8461840642724514 \cdot 10^{164}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r1639 = x;
        double r1640 = y;
        double r1641 = z;
        double r1642 = t;
        double r1643 = r1641 - r1642;
        double r1644 = r1640 * r1643;
        double r1645 = a;
        double r1646 = r1644 / r1645;
        double r1647 = r1639 + r1646;
        return r1647;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1648 = y;
        double r1649 = z;
        double r1650 = t;
        double r1651 = r1649 - r1650;
        double r1652 = r1648 * r1651;
        double r1653 = -3.2688106303761396e+233;
        bool r1654 = r1652 <= r1653;
        double r1655 = x;
        double r1656 = a;
        double r1657 = r1648 / r1656;
        double r1658 = 1.0;
        double r1659 = r1658 / r1651;
        double r1660 = r1657 / r1659;
        double r1661 = r1655 + r1660;
        double r1662 = 2.8461840642724514e+164;
        bool r1663 = r1652 <= r1662;
        double r1664 = r1652 / r1656;
        double r1665 = r1655 + r1664;
        double r1666 = r1656 / r1651;
        double r1667 = r1648 / r1666;
        double r1668 = r1655 + r1667;
        double r1669 = r1663 ? r1665 : r1668;
        double r1670 = r1654 ? r1661 : r1669;
        return r1670;
}

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
Target0.7
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)) < -3.2688106303761396e+233

    1. Initial program 34.4

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

    3. Applied associate-/l*0.5

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

    5. Applied div-inv0.5

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

    6. Applied associate-/r*0.3

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

    if -3.2688106303761396e+233 < (* y (- z t)) < 2.8461840642724514e+164

    1. Initial program 0.4

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

    if 2.8461840642724514e+164 < (* y (- z t))

    1. Initial program 23.2

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

    3. Applied associate-/l*1.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -3.2688106303761396 \cdot 10^{233}:\\ \;\;\;\;x + \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.8461840642724514 \cdot 10^{164}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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)))