Average Error: 2.8 → 1.3
Time: 9.9s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) (((double) (1.0 / ((double) sqrt(((double) M_PI))))) * ((double) exp(((double) (((double) fabs(x)) * ((double) fabs(x)))))))) * ((double) (((double) (((double) (((double) (1.0 / ((double) fabs(x)))) + ((double) (((double) (1.0 / 2.0)) * ((double) (((double) (((double) (1.0 / ((double) fabs(x)))) * ((double) (1.0 / ((double) fabs(x)))))) * ((double) (1.0 / ((double) fabs(x)))))))))) + ((double) (((double) (3.0 / 4.0)) * ((double) (((double) (((double) (((double) (((double) (1.0 / ((double) fabs(x)))) * ((double) (1.0 / ((double) fabs(x)))))) * ((double) (1.0 / ((double) fabs(x)))))) * ((double) (1.0 / ((double) fabs(x)))))) * ((double) (1.0 / ((double) fabs(x)))))))))) + ((double) (((double) (15.0 / 8.0)) * ((double) (((double) (((double) (((double) (((double) (((double) (((double) (1.0 / ((double) fabs(x)))) * ((double) (1.0 / ((double) fabs(x)))))) * ((double) (1.0 / ((double) fabs(x)))))) * ((double) (1.0 / ((double) fabs(x)))))) * ((double) (1.0 / ((double) fabs(x)))))) * ((double) (1.0 / ((double) fabs(x)))))) * ((double) (1.0 / ((double) fabs(x))))))))))));
}

↓
double code(double x) {
	return ((double) (((double) (1.0 / ((double) sqrt(((double) M_PI))))) * ((double) (((double) pow(((double) exp(((double) fabs(x)))), ((double) fabs(x)))) * ((double) (((double) (1.0 / ((double) fabs(x)))) + ((double) (((double) (((double) (1.0 / 2.0)) * ((double) (((double) pow(((double) pow(((double) sqrt(((double) (1.0 / ((double) fabs(x)))))), ((double) sqrt(3.0)))), ((double) sqrt(3.0)))) * ((double) pow(((double) pow(((double) sqrt(((double) (1.0 / ((double) fabs(x)))))), ((double) sqrt(3.0)))), ((double) sqrt(3.0)))))))) + ((double) (((double) (((double) (3.0 / 4.0)) * ((double) pow(((double) (1.0 / ((double) fabs(x)))), 5.0)))) + ((double) (((double) (15.0 / 8.0)) * ((double) (1.0 / ((double) pow(((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 2.8
    \[\]
  2. Simplified1.4
    \[\leadsto \]
  3. Taylor expanded around 0 1.3
    \[\leadsto \]
  4. Using strategy rm
  5. Applied add-sqr-sqrt1.3
    \[\leadsto \]
  6. Applied pow-unpow1.3
    \[\leadsto \]
  7. Using strategy rm
  8. Applied add-sqr-sqrt1.3
    \[\leadsto \]
  9. Applied unpow-prod-down1.3
    \[\leadsto \]
  10. Applied unpow-prod-down1.3
    \[\leadsto \]
  11. Final simplification1.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x)
  :name "Jmat.Real.erfi, branch x greater than or equal to 5"
  :precision binary64
  :pre (>= x 0.5)
  (* (* (/ 1.0 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1.0 (fabs x)) (* (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 3.0 4.0) (* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 15.0 8.0) (* (* (* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))))))