Numeric.Signal:interpolate from hsignal-0.2.7.1

Average Error: 15.1 → 11.0

Time: 7.9s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.8506421456968734 \cdot 10^{-283}:\\ \;\;\;\;x + {\left(\frac{\left(y - z\right) \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{{\left(\sqrt[3]{\sqrt[3]{a - z}}\right)}^{3}}\right)}^{1} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 3.38756528908946904 \cdot 10^{-258}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array}\]

C

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 VAR;
	if (((x + ((y - z) * ((t - x) / (a - z)))) <= -1.8506421456968734e-283)) {
		VAR = (x + (pow(((((y - z) * cbrt((t - x))) / cbrt((a - z))) * (cbrt((t - x)) / pow(cbrt(cbrt((a - z))), 3.0))), 1.0) * (cbrt((t - x)) / cbrt((a - z)))));
	} else {
		double VAR_1;
		if (((x + ((y - z) * ((t - x) / (a - z)))) <= 3.387565289089469e-258)) {
			VAR_1 = ((((x * y) / z) + t) - ((t * y) / z));
		} else {
			VAR_1 = (x + ((y - z) * ((t - x) / (a - z))));
		}
		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)))) < -1.8506421456968734e-283

   1. Initial program 7.3

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

   3. Applied add-cube-cbrt 8.0

      \[\leadsto x + \left(y - z\right) \cdot \frac{t - x}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}}\]

   4. Applied add-cube-cbrt 8.1

      \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}\]

   5. Applied times-frac 8.1

      \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right)}\]

   6. Applied associate-*r* 4.6

      \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}}\]
   7. Using strategy rm

   8. Applied add-cube-cbrt 4.7

      \[\leadsto x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}\right) \cdot \sqrt[3]{\sqrt[3]{a - z}}\right)}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\]

   9. Applied associate-*r* 4.7

      \[\leadsto x + \left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \left(\sqrt[3]{\sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{a - z}}}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\]
   10. Using strategy rm

   11. Applied pow1 4.7

       \[\leadsto x + \left(\left(y - z\right) \cdot \color{blue}{{\left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\left(\sqrt[3]{a - z} \cdot \left(\sqrt[3]{\sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{a - z}}}\right)}^{1}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\]

   12. Applied pow1 4.7

       \[\leadsto x + \left(\color{blue}{{\left(y - z\right)}^{1}} \cdot {\left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\left(\sqrt[3]{a - z} \cdot \left(\sqrt[3]{\sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{a - z}}}\right)}^{1}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\]

   13. Applied pow-prod-down 4.7

       \[\leadsto x + \color{blue}{{\left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\left(\sqrt[3]{a - z} \cdot \left(\sqrt[3]{\sqrt[3]{a - z}} \cdot \sqrt[3]{\sqrt[3]{a - z}}\right)\right) \cdot \sqrt[3]{\sqrt[3]{a - z}}}\right)}^{1}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\]

   14. Simplified 9.3

       \[\leadsto x + {\color{blue}{\left(\frac{\left(y - z\right) \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{{\left(\sqrt[3]{\sqrt[3]{a - z}}\right)}^{3}}\right)}}^{1} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\]

   if -1.8506421456968734e-283 < (+ x (* (- y z) (/ (- t x) (- a z)))) < 3.387565289089469e-258

   1. Initial program 58.9

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

   2. Taylor expanded around inf 26.9

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

   if 3.387565289089469e-258 < (+ x (* (- y z) (/ (- t x) (- a z))))

   1. Initial program 6.8

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

4. Final simplification 11.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le -1.8506421456968734 \cdot 10^{-283}:\\ \;\;\;\;x + {\left(\frac{\left(y - z\right) \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{{\left(\sqrt[3]{\sqrt[3]{a - z}}\right)}^{3}}\right)}^{1} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \le 3.38756528908946904 \cdot 10^{-258}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 
(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)))))