(if (< x 0.5) (+ L (* (- H L) x)) (- H (* (- H L) (- 1 x))))

Average Error: 0.0 → 0.0

Time: 1.1s

Precision: binary64

Math

\[\begin{array}{l} \mathbf{if}\;x \lt 0.5:\\ \;\;\;\;L + \left(H - L\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;H - \left(H - L\right) \cdot \left(1 - x\right)\\ \end{array}\]

↓

\[\begin{array}{l} \mathbf{if}\;x \lt 0.5:\\ \;\;\;\;L + \left(H - L\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;H - \left(H - L\right) \cdot \left(1 - x\right)\\ \end{array}\]

C

double code(double x, double L, double H) {
	double VAR;
	if ((x < 0.5)) {
		VAR = ((double) (L + ((double) (((double) (H - L)) * x))));
	} else {
		VAR = ((double) (H - ((double) (((double) (H - L)) * ((double) (1.0 - x))))));
	}
	return VAR;
}

↓

double code(double x, double L, double H) {
	double VAR;
	if ((x < 0.5)) {
		VAR = ((double) (L + ((double) (((double) (H - L)) * x))));
	} else {
		VAR = ((double) (H - ((double) (((double) (H - L)) * ((double) (1.0 - x))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus L

Bits error versus H

Derivation

1. Initial program 0.0

   \[\begin{array}{l} \mathbf{if}\;x \lt 0.5:\\ \;\;\;\;L + \left(H - L\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;H - \left(H - L\right) \cdot \left(1 - x\right)\\ \end{array}\]

2. Final simplification 0.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \lt 0.5:\\ \;\;\;\;L + \left(H - L\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;H - \left(H - L\right) \cdot \left(1 - x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x L H)
  :name "(if (< x 0.5) (+ L (* (- H L) x)) (- H (* (- H L) (- 1 x))))"
  :precision binary64
  (if (< x 0.5) (+ L (* (- H L) x)) (- H (* (- H L) (- 1.0 x)))))