(/ (* (* (* (/ (+ myTopRad myBotRad) 2.0) 2.0) PI) myTurns) numPts)

Average Error: 7.0 → 1.7

Time: 2.0s

Precision: binary64

Math

\[\frac{\left(\left(\frac{myTopRad + myBotRad}{2} \cdot 2\right) \cdot \pi\right) \cdot myTurns}{numPts}\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(\frac{myTopRad + myBotRad}{2} \cdot 2\right) \cdot \pi\right) \cdot myTurns \le -2.6799121723130699 \cdot 10^{151} \lor \neg \left(\left(\left(\frac{myTopRad + myBotRad}{2} \cdot 2\right) \cdot \pi\right) \cdot myTurns \le 2.811051946843951 \cdot 10^{221}\right):\\ \;\;\;\;\left(\frac{myTurns}{numPts} \cdot \left(myTopRad + myBotRad\right)\right) \cdot \pi\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(\frac{myTopRad + myBotRad}{2} \cdot 2\right) \cdot \pi\right) \cdot myTurns}{numPts}\\ \end{array}\]

C

double code(double myTopRad, double myBotRad, double myTurns, double numPts) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (myTopRad + myBotRad)) / 2.0)) * 2.0)) * ((double) M_PI))) * myTurns)) / numPts));
}

↓

double code(double myTopRad, double myBotRad, double myTurns, double numPts) {
	double VAR;
	if (((((double) (((double) (((double) (((double) (((double) (myTopRad + myBotRad)) / 2.0)) * 2.0)) * ((double) M_PI))) * myTurns)) <= -2.67991217231307e+151) || !(((double) (((double) (((double) (((double) (((double) (myTopRad + myBotRad)) / 2.0)) * 2.0)) * ((double) M_PI))) * myTurns)) <= 2.811051946843951e+221))) {
		VAR = ((double) (((double) (((double) (myTurns / numPts)) * ((double) (myTopRad + myBotRad)))) * ((double) M_PI)));
	} else {
		VAR = ((double) (((double) (((double) (((double) (((double) (((double) (myTopRad + myBotRad)) / 2.0)) * 2.0)) * ((double) M_PI))) * myTurns)) / numPts));
	}
	return VAR;
}

Error

Bits error versus myTopRad

Bits error versus myBotRad

Bits error versus myTurns

Bits error versus numPts

Derivation

1. Split input into 2 regimes

2. if (* (* (* (/ (+ myTopRad myBotRad) 2.0) 2.0) PI) myTurns) < -2.6799121723130699e151 or 2.811051946843951e221 < (* (* (* (/ (+ myTopRad myBotRad) 2.0) 2.0) PI) myTurns)

   1. Initial program 25.5

      \[\frac{\left(\left(\frac{myTopRad + myBotRad}{2} \cdot 2\right) \cdot \pi\right) \cdot myTurns}{numPts}\]

   2. Simplified 1.6

      \[\leadsto \color{blue}{\left(\frac{myTurns}{numPts} \cdot \left(myTopRad + myBotRad\right)\right) \cdot \pi}\]

   if -2.6799121723130699e151 < (* (* (* (/ (+ myTopRad myBotRad) 2.0) 2.0) PI) myTurns) < 2.811051946843951e221

   1. Initial program 1.7

      \[\frac{\left(\left(\frac{myTopRad + myBotRad}{2} \cdot 2\right) \cdot \pi\right) \cdot myTurns}{numPts}\]
3. Recombined 2 regimes into one program.

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\frac{myTopRad + myBotRad}{2} \cdot 2\right) \cdot \pi\right) \cdot myTurns \le -2.6799121723130699 \cdot 10^{151} \lor \neg \left(\left(\left(\frac{myTopRad + myBotRad}{2} \cdot 2\right) \cdot \pi\right) \cdot myTurns \le 2.811051946843951 \cdot 10^{221}\right):\\ \;\;\;\;\left(\frac{myTurns}{numPts} \cdot \left(myTopRad + myBotRad\right)\right) \cdot \pi\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(\frac{myTopRad + myBotRad}{2} \cdot 2\right) \cdot \pi\right) \cdot myTurns}{numPts}\\ \end{array}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (myTopRad myBotRad myTurns numPts)
  :name "(/ (* (* (* (/ (+ myTopRad myBotRad) 2.0) 2.0) PI) myTurns) numPts)"
  :precision binary64
  (/ (* (* (* (/ (+ myTopRad myBotRad) 2.0) 2.0) PI) myTurns) numPts))