Average Error: 14.8 → 10.2
Time: 4.7s
Precision: 64
\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -9.88656814146117223 \cdot 10^{-154} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 4.73247773315875748 \cdot 10^{-210}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\ \end{array}\]
x + \left(y - z\right) \cdot \frac{t - x}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -9.88656814146117223 \cdot 10^{-154} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 4.73247773315875748 \cdot 10^{-210}\right):\\
\;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return (x + ((y - z) * ((t - x) / (a - z))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double temp;
	if ((((x + ((y - z) * ((t - x) / (a - z)))) <= -9.886568141461172e-154) || !((x + ((y - z) * ((t - x) / (a - z)))) <= 4.7324777331587575e-210))) {
		temp = (x + ((y - z) * ((t - x) / (a - z))));
	} else {
		temp = fma(y, ((x / z) - (t / z)), t);
	}
	return temp;
}

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

Derivation

  1. Split input into 2 regimes

  2. if (+ x (* (- y z) (/ (- t x) (- a z)))) < -9.886568141461172e-154 or 4.7324777331587575e-210 < (+ x (* (- y z) (/ (- t x) (- a z))))

    1. Initial program 6.1

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

    if -9.886568141461172e-154 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 4.7324777331587575e-210

    1. Initial program 50.4

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

    2. Simplified50.1

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

    3. Taylor expanded around inf 29.8

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

    4. Simplified27.2

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification10.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -9.88656814146117223 \cdot 10^{-154} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 4.73247773315875748 \cdot 10^{-210}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x}{z} - \frac{t}{z}, t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))