Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 14.7 → 9.8

Time: 5.9s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -3.8916707755875982 \cdot 10^{-50}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(\left(t - x\right) \cdot \frac{1}{a - z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -5.92656601179197108 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 9.1660507532031028 \cdot 10^{-134}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(\left(t - x\right) \cdot \frac{1}{a - z}\right)\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y - z)) * ((double) (((double) (t - x)) / ((double) (a - z))))))));
}

↓

double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((double) (x + ((double) (((double) (y - z)) * ((double) (((double) (t - x)) / ((double) (a - z)))))))) <= -3.891670775587598e-50)) {
		VAR = ((double) (x + ((double) (((double) (y - z)) * ((double) (((double) (t - x)) * ((double) (1.0 / ((double) (a - z))))))))));
	} else {
		double VAR_1;
		if ((((double) (x + ((double) (((double) (y - z)) * ((double) (((double) (t - x)) / ((double) (a - z)))))))) <= -5.926566011791971e-284)) {
			VAR_1 = ((double) (x + ((double) (((double) (((double) (y - z)) * ((double) (t - x)))) / ((double) (a - z))))));
		} else {
			double VAR_2;
			if ((((double) (x + ((double) (((double) (y - z)) * ((double) (((double) (t - x)) / ((double) (a - z)))))))) <= 9.166050753203103e-134)) {
				VAR_2 = ((double) (t + ((double) (y * ((double) (((double) (x / z)) - ((double) (t / z))))))));
			} else {
				VAR_2 = ((double) (x + ((double) (((double) (y - z)) * ((double) (((double) (t - x)) * ((double) (1.0 / ((double) (a - z))))))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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 3 regimes

2. if (+ x (* (- y z) (/ (- t x) (- a z)))) < -3.8916707755875982e-50 or 9.1660507532031028e-134 < (+ x (* (- y z) (/ (- t x) (- a z))))

   1. Initial program 5.3

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

   3. Applied div-inv 5.4

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

   if -3.8916707755875982e-50 < (+ x (* (- y z) (/ (- t x) (- a z)))) < -5.92656601179197108e-284

   1. Initial program 15.8

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

   3. Applied associate-*r/ 7.8

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

   if -5.92656601179197108e-284 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 9.1660507532031028e-134

   1. Initial program 50.1

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

   2. Taylor expanded around inf 30.6

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

   3. Simplified 27.3

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

4. Final simplification 9.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -3.8916707755875982 \cdot 10^{-50}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(\left(t - x\right) \cdot \frac{1}{a - z}\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -5.92656601179197108 \cdot 10^{-284}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 9.1660507532031028 \cdot 10^{-134}:\\ \;\;\;\;t + y \cdot \left(\frac{x}{z} - \frac{t}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \left(\left(t - x\right) \cdot \frac{1}{a - z}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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)))))