Average Error: 14.7 → 13.9
Time: 23.4s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 4.414999570783422340397446628721574989275 \cdot 10^{213}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{a - z} \cdot \left(t - x\right), y - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;z \le 4.414999570783422340397446628721574989275 \cdot 10^{213}:\\
\;\;\;\;\mathsf{fma}\left(\frac{1}{a - z} \cdot \left(t - x\right), y - z, x\right)\\

\mathbf{else}:\\
\;\;\;\;t\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r4587535 = x;
        double r4587536 = y;
        double r4587537 = z;
        double r4587538 = r4587536 - r4587537;
        double r4587539 = t;
        double r4587540 = r4587539 - r4587535;
        double r4587541 = a;
        double r4587542 = r4587541 - r4587537;
        double r4587543 = r4587540 / r4587542;
        double r4587544 = r4587538 * r4587543;
        double r4587545 = r4587535 + r4587544;
        return r4587545;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r4587546 = z;
        double r4587547 = 4.4149995707834223e+213;
        bool r4587548 = r4587546 <= r4587547;
        double r4587549 = 1.0;
        double r4587550 = a;
        double r4587551 = r4587550 - r4587546;
        double r4587552 = r4587549 / r4587551;
        double r4587553 = t;
        double r4587554 = x;
        double r4587555 = r4587553 - r4587554;
        double r4587556 = r4587552 * r4587555;
        double r4587557 = y;
        double r4587558 = r4587557 - r4587546;
        double r4587559 = fma(r4587556, r4587558, r4587554);
        double r4587560 = r4587548 ? r4587559 : r4587553;
        return r4587560;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Derivation

  1. Split input into 2 regimes

  2. if z < 4.4149995707834223e+213

    1. Initial program 12.9

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

    2. Simplified12.8

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

    4. Applied div-inv12.9

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

    if 4.4149995707834223e+213 < z

    1. Initial program 32.1

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

    2. Simplified32.0

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

    3. Taylor expanded around 0 23.6

      \[\leadsto \color{blue}{t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification13.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 4.414999570783422340397446628721574989275 \cdot 10^{213}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{a - z} \cdot \left(t - x\right), y - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  (+ x (* (- y z) (/ (- t x) (- a z)))))