Average Error: 0.2 → 0.2
Time: 4.7s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) fabs(((double) (((double) (1.0 / ((double) sqrt(((double) M_PI))))) * ((double) (((double) (((double) (((double) (2.0 * ((double) fabs(x)))) + ((double) (((double) (2.0 / 3.0)) * ((double) (((double) (((double) fabs(x)) * ((double) fabs(x)))) * ((double) fabs(x)))))))) + ((double) (((double) (1.0 / 5.0)) * ((double) (((double) (((double) (((double) (((double) fabs(x)) * ((double) fabs(x)))) * ((double) fabs(x)))) * ((double) fabs(x)))) * ((double) fabs(x)))))))) + ((double) (((double) (1.0 / 21.0)) * ((double) (((double) (((double) (((double) (((double) (((double) (((double) fabs(x)) * ((double) fabs(x)))) * ((double) fabs(x)))) * ((double) fabs(x)))) * ((double) fabs(x)))) * ((double) fabs(x)))) * ((double) fabs(x))))))))))));
}

↓
double code(double x) {
	return ((double) fabs(((double) (((double) (1.0 / ((double) sqrt(((double) M_PI))))) * ((double) (((double) (2.0 * ((double) (((double) fabs(x)) + ((double) (((double) pow(((double) fabs(x)), 3.0)) / 3.0)))))) + ((double) (1.0 * ((double) (((double) (((double) pow(((double) fabs(x)), 5.0)) / 5.0)) + ((double) (((double) pow(((double) sqrt(((double) fabs(x)))), 7.0)) / ((double) (21.0 / ((double) pow(((double) sqrt(((double) fabs(x)))), 7.0))))))))))))))));
}

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. Using strategy rm
  4. Applied add-sqr-sqrt0.2
    \[\leadsto \]
  5. Applied unpow-prod-down0.2
    \[\leadsto \]
  6. Applied associate-/l*0.2
    \[\leadsto \]
  7. Final simplification0.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(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)))))))