Average Error: 47.9 → 15.0
Time: 14.1s
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 <= -0.13914382206341622)) {
		VAR = ((double) (((double) (n * ((double) (100.0 * ((double) (((double) pow(((double) (1.0 + ((double) (i / n)))), n)) - 1.0)))))) / i));
	} else {
		double VAR_1;
		if ((i <= 315.5800385030618)) {
			VAR_1 = ((double) (100.0 * ((double) (n * ((double) (((double) (((double) cbrt(((double) (((double) (((double) (((double) log(1.0)) * ((double) (n - ((double) (i * ((double) (i * 0.5)))))))) + ((double) (i * ((double) (1.0 + ((double) (i * 0.5)))))))) / i)))) * ((double) cbrt(((double) (((double) (((double) (((double) log(1.0)) * ((double) (n - ((double) (i * ((double) (i * 0.5)))))))) + ((double) (i * ((double) (1.0 + ((double) (i * 0.5)))))))) / i)))))) * ((double) cbrt(((double) (((double) cbrt(((double) (((double) (((double) (((double) log(1.0)) * ((double) (n - ((double) (i * ((double) (i * 0.5)))))))) + ((double) (i * ((double) (1.0 + ((double) (i * 0.5)))))))) / i)))) * ((double) (((double) cbrt(((double) (((double) (((double) (((double) log(1.0)) * ((double) (n - ((double) (i * ((double) (i * 0.5)))))))) + ((double) (i * ((double) (1.0 + ((double) (i * 0.5)))))))) / i)))) * ((double) cbrt(((double) (((double) (((double) (((double) log(1.0)) * ((double) (n - ((double) (i * ((double) (i * 0.5)))))))) + ((double) (i * ((double) (1.0 + ((double) (i * 0.5)))))))) / i))))))))))))))));
		} else {
			VAR_1 = ((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) (50.0 * ((double) (((double) pow(((double) log(n)), 2.0)) * ((double) (((double) pow(n, 3.0)) / i)))))) + ((double) (100.0 * ((double) (((double) (((double) (((double) log(1.0)) / i)) * ((double) (((double) log(i)) * ((double) pow(n, 3.0)))))) + ((double) (((double) (n * n)) * ((double) (((double) log(i)) / i)))))))))))))))) + ((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) (100.0 * ((double) (((double) (((double) pow(n, 3.0)) * ((double) log(n)))) * ((double) (((double) (((double) log(1.0)) / i)) + ((double) (((double) log(i)) / i)))))))) + ((double) (50.0 * ((double) (((double) (((double) (((double) pow(((double) log(1.0)), 2.0)) / i)) * ((double) (((double) pow(n, 4.0)) * ((double) log(n)))))) + ((double) (((double) (((double) pow(((double) log(i)), 2.0)) / i)) * ((double) (((double) pow(n, 4.0)) * ((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 = 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
Original47.9
Target47.5
Herbie15.0
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  i  < -0.139143822063416217
    1. Initial program 28.0
      \[\]
    2. Simplified28.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied associate-*r/28.7
      \[\leadsto \]
    5. Applied associate-*r/28.7
      \[\leadsto \]
    6. Simplified28.7
      \[\leadsto \]
    if -0.139143822063416217 <  i  < 315.58003850306181
    1. Initial program 58.3
      \[\]
    2. Simplified57.9
      \[\leadsto \]
    3. Taylor expanded around 0 9.1
      \[\leadsto \]
    4. Simplified9.1
      \[\leadsto \]
    5. Using strategy rm
    6. Applied add-cube-cbrt9.2
      \[\leadsto \]
    7. Simplified9.2
      \[\leadsto \]
    8. Simplified9.2
      \[\leadsto \]
    9. Using strategy rm
    10. Applied add-cube-cbrt9.2
      \[\leadsto \]
    if 315.58003850306181 <  i 
    1. Initial program 31.7
      \[\]
    2. Simplified31.7
      \[\leadsto \]
    3. Taylor expanded around 0 19.9
      \[\leadsto \]
    4. Simplified20.0
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification15.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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))))