Average Error: 47.7 → 15.3
Time: 13.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double i, double n) {
	return ((double) (100.0 * ((double) (((double) (((double) pow(((double) (1.0 + ((double) (i / n)))), n)) - 1.0)) / ((double) (i / n))))));
}

↓
double code(double i, double n) {
	double VAR;
	if ((i <= -5.254825670150266e-11)) {
		VAR = ((double) (100.0 * ((double) (((double) (n * ((double) (((double) pow(((double) (1.0 + ((double) (i / n)))), n)) - 1.0)))) / i))));
	} else {
		double VAR_1;
		if ((i <= -4.9797303581472035e-204)) {
			VAR_1 = ((double) (((double) (n * ((double) (100.0 * ((double) (((double) (i * 1.0)) + ((double) (((double) (n * ((double) log(1.0)))) + ((double) (((double) (i * i)) * ((double) (0.5 - ((double) (((double) log(1.0)) * 0.5)))))))))))))) / i));
		} else {
			double VAR_2;
			if ((i <= 0.00017000305165270794)) {
				VAR_2 = ((double) (n * ((double) (100.0 * ((double) (((double) (((double) (i * 1.0)) + ((double) (((double) (n * ((double) log(1.0)))) + ((double) (((double) (i * i)) * ((double) (0.5 - ((double) (((double) log(1.0)) * 0.5)))))))))) / i))))));
			} else {
				VAR_2 = ((double) (((double) (((double) (((double) (((double) pow(((double) log(1.0)), 2.0)) / i)) * ((double) (((double) log(i)) * ((double) pow(n, 4.0)))))) * 49.99999999999999)) + ((double) (((double) (((double) (((double) (((double) pow(((double) log(1.0)), 2.0)) / i)) * ((double) pow(n, 3.0)))) * 50.0)) + ((double) (((double) (((double) (((double) (((double) pow(n, 4.0)) * ((double) (((double) pow(((double) log(1.0)), 3.0)) / i)))) * 16.666666666666664)) + ((double) (((double) (100.0 * ((double) (((double) (((double) log(1.0)) / i)) * ((double) (n * n)))))) + ((double) (((double) (((double) (49.99999999999999 * ((double) (((double) (((double) log(1.0)) / i)) * ((double) (((double) pow(n, 4.0)) * ((double) pow(((double) log(i)), 2.0)))))))) + ((double) (((double) (16.666666666666664 * ((double) (((double) pow(n, 4.0)) * ((double) (((double) pow(((double) log(i)), 3.0)) / i)))))) + ((double) (((double) (50.0 * ((double) (((double) (((double) log(i)) / i)) * ((double) (((double) pow(n, 4.0)) * ((double) pow(((double) log(n)), 2.0)))))))) + ((double) (((double) (100.0 * ((double) (((double) (n * n)) * ((double) (((double) log(i)) / i)))))) + ((double) (((double) (50.0 * ((double) (((double) pow(((double) log(n)), 2.0)) * ((double) (((double) pow(n, 3.0)) / i)))))) + ((double) (100.0 * ((double) (((double) (((double) log(1.0)) / i)) * ((double) (((double) log(i)) * ((double) pow(n, 3.0)))))))))))))))))) + ((double) (50.0 * ((double) (((double) (((double) (((double) log(1.0)) / i)) * ((double) (((double) pow(n, 4.0)) * ((double) pow(((double) log(n)), 2.0)))))) + ((double) (((double) pow(n, 3.0)) * ((double) (((double) pow(((double) log(i)), 2.0)) / i)))))))))))))) - ((double) (((double) (16.666666666666664 * ((double) (((double) (((double) pow(n, 4.0)) / i)) * ((double) pow(((double) log(n)), 3.0)))))) + ((double) (((double) (((double) (50.0 * ((double) (((double) (((double) pow(((double) log(i)), 2.0)) / i)) * ((double) (((double) pow(n, 4.0)) * ((double) log(n)))))))) + ((double) (((double) (50.0 * ((double) (((double) (((double) pow(((double) log(1.0)), 2.0)) / i)) * ((double) (((double) pow(n, 4.0)) * ((double) log(n)))))))) + ((double) (100.0 * ((double) (((double) (((double) (((double) log(1.0)) / i)) * ((double) (((double) pow(n, 3.0)) * ((double) log(n)))))) + ((double) (((double) (((double) log(i)) / i)) * ((double) (((double) pow(n, 3.0)) * ((double) log(n)))))))))))))) + ((double) (100.0 * ((double) (((double) (((double) log(n)) * ((double) (((double) (n * n)) / i)))) + ((double) (((double) (((double) log(1.0)) / i)) * ((double) (((double) (((double) log(i)) * ((double) pow(n, 4.0)))) * ((double) log(n))))))))))))))))))));
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus i
Bits error versus n
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original47.7
Target47.4
Herbie15.3
\[\]
Derivation
  1. Split input into 4 regimes
  2. if  i  < -5.2548256701502658e-11
    1. Initial program 29.1
      \[\]
    2. Simplified29.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied associate-*r/29.7
      \[\leadsto \]
    if -5.2548256701502658e-11 <  i  < -4.97973035814720355e-204
    1. Initial program 56.2
      \[\]
    2. Simplified56.0
      \[\leadsto \]
    3. Taylor expanded around 0 12.2
      \[\leadsto \]
    4. Simplified12.2
      \[\leadsto \]
    5. Using strategy rm
    6. Applied associate-*r/9.9
      \[\leadsto \]
    7. Applied associate-*r/10.1
      \[\leadsto \]
    8. Simplified10.0
      \[\leadsto \]
    if -4.97973035814720355e-204 <  i  < 1.7000305165270794e-4
    1. Initial program 58.9
      \[\]
    2. Simplified58.6
      \[\leadsto \]
    3. Taylor expanded around 0 7.6
      \[\leadsto \]
    4. Simplified7.6
      \[\leadsto \]
    5. Using strategy rm
    6. Applied pow17.6
      \[\leadsto \]
    7. Applied pow17.6
      \[\leadsto \]
    8. Applied pow-prod-down7.6
      \[\leadsto \]
    9. Applied pow17.6
      \[\leadsto \]
    10. Applied pow-prod-down7.6
      \[\leadsto \]
    11. Simplified7.6
      \[\leadsto \]
    if 1.7000305165270794e-4 <  i 
    1. Initial program 32.0
      \[\]
    2. Simplified32.0
      \[\leadsto \]
    3. Taylor expanded around 0 21.9
      \[\leadsto \]
    4. Simplified22.0
      \[\leadsto \]
  3. Recombined 4 regimes into one program.
  4. Final simplification15.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (i n)
  :name "Compound Interest"
  :precision binary64

  :herbie-target
  (* 100.0 (/ (- (exp (* n (if (== (+ 1.0 (/ i n)) 1.0) (/ i n) (/ (* (/ i n) (log (+ 1.0 (/ i n)))) (- (+ (/ i n) 1.0) 1.0))))) 1.0) (/ i n)))

  (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))