Average Error: 6.1 → 0.4
Time: 20.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y = -\infty:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;\left(z - t\right) \cdot y \le 2.8419260078404496 \cdot 10^{+233}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;\left(z - t\right) \cdot y = -\infty:\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

\mathbf{elif}\;\left(z - t\right) \cdot y \le 2.8419260078404496 \cdot 10^{+233}:\\
\;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r16753767 = x;
        double r16753768 = y;
        double r16753769 = z;
        double r16753770 = t;
        double r16753771 = r16753769 - r16753770;
        double r16753772 = r16753768 * r16753771;
        double r16753773 = a;
        double r16753774 = r16753772 / r16753773;
        double r16753775 = r16753767 + r16753774;
        return r16753775;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r16753776 = z;
        double r16753777 = t;
        double r16753778 = r16753776 - r16753777;
        double r16753779 = y;
        double r16753780 = r16753778 * r16753779;
        double r16753781 = -inf.0;
        bool r16753782 = r16753780 <= r16753781;
        double r16753783 = x;
        double r16753784 = a;
        double r16753785 = r16753779 / r16753784;
        double r16753786 = r16753785 * r16753778;
        double r16753787 = r16753783 + r16753786;
        double r16753788 = 2.8419260078404496e+233;
        bool r16753789 = r16753780 <= r16753788;
        double r16753790 = r16753780 / r16753784;
        double r16753791 = r16753783 + r16753790;
        double r16753792 = r16753789 ? r16753791 : r16753787;
        double r16753793 = r16753782 ? r16753787 : r16753792;
        return r16753793;
}

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
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -inf.0 or 2.8419260078404496e+233 < (* y (- z t))

    1. Initial program 44.2

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

    2. Simplified0.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef0.3

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

    if -inf.0 < (* y (- z t)) < 2.8419260078404496e+233

    1. Initial program 0.4

      \[x + \frac{y \cdot \left(z - t\right)}{a}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y = -\infty:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;\left(z - t\right) \cdot y \le 2.8419260078404496 \cdot 10^{+233}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \end{array}\]

Reproduce

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

  :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)))