Average Error: 29.2 → 0.4
Time: 3.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double a, double x) {
	return ((double) (((double) exp(((double) (a * x)))) - 1.0));
}

↓
double code(double a, double x) {
	double VAR;
	if ((((double) (a * x)) <= -0.0003443200474434158)) {
		VAR = ((double) (((double) exp(((double) (a * x)))) - 1.0));
	} else {
		VAR = ((double) (((double) (a * x)) + ((double) (a * ((double) (x * ((double) (a * ((double) (x * 0.5))))))))));
	}
	return VAR;
}

Error
Bits error versus a
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original29.2
Target0.2
Herbie0.4
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  (* a x)  < -3.443200474434158e-4
    1. Initial program 0.0
      \[\]
    if -3.443200474434158e-4 <  (* a x) 
    1. Initial program 44.4
      \[\]
    2. Taylor expanded around 0 14.4
      \[\leadsto \]
    3. Simplified8.0
      \[\leadsto \]
    4. Taylor expanded around 0 8.3
      \[\leadsto \]
    5. Simplified4.4
      \[\leadsto \]
    6. Using strategy rm
    7. Applied associate-*r*0.5
      \[\leadsto \]
    8. Simplified0.5
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (a x)
  :name "expax (section 3.5)"
  :precision binary64
  :herbie-expected 14

  :herbie-target
  (if (< (fabs (* a x)) 0.1) (* (* a x) (+ 1.0 (+ (/ (* a x) 2.0) (/ (pow (* a x) 2.0) 6.0)))) (- (exp (* a x)) 1.0))

  (- (exp (* a x)) 1.0))