Average Error: 0.2 → 0.2
Time: 7.2s
Precision: binary64
\[\]
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↓
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↓
double code(double x) {
	return fabs((1.0 / sqrt((double) M_PI)) * ((((2.0 * fabs(x)) + ((2.0 / 3.0) * ((fabs(x) * fabs(x)) * fabs(x)))) + ((1.0 / 5.0) * ((((fabs(x) * fabs(x)) * fabs(x)) * fabs(x)) * fabs(x)))) + ((1.0 / 21.0) * ((((((fabs(x) * fabs(x)) * fabs(x)) * fabs(x)) * fabs(x)) * fabs(x)) * fabs(x)))));
}

↓
double code(double x) {
	return fabs(1.0 * (((pow(fabs(x), 7.0) * 0.047619047619047616) + ((pow(fabs(x), 5.0) * 0.2) + ((pow(fabs(x), 3.0) * 0.6666666666666666) + (fabs(x) * 2.0)))) * sqrt(1.0 / ((double) M_PI))));
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 0.2
    \[\]
  2. Simplified0.1
    \[\leadsto \]
  3. Taylor expanded around 0 0.2
    \[\leadsto \]
  4. Simplified0.2
    \[\leadsto \]
  5. Final simplification0.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020338 
(FPCore (x)
  :name "Jmat.Real.erfi, branch x less than or equal to 0.5"
  :precision binary64
  :pre (<= x 0.5)
  (fabs (* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))))