


Bits error versus x
Results
Initial program 1.5
rmApplied frac-times1.3
Simplified1.3
Simplified1.0
rmApplied pow21.0
Applied pow11.0
Applied pow11.0
Applied pow-prod-up1.0
Applied pow11.0
Applied pow-flip1.0
Applied pow-div0.8
Applied pow-div0.7
Simplified0.7
Final simplification0.7
herbie shell --seed 2018365
(FPCore (x)
:name "Jmat.Real.erfi, branch x greater than or equal to 5"
(* (* (/ 1 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (* (/ 1 2) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 3 4) (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 15 8) (* (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x)))))))
Time bar (total: 1.1m)Debug log
2 alts after pruning (2 fresh and 0 done)
Merged error: 1.2b
Found 4 expressions with local error:
| 1.0b | (sqrt PI) |
| 0.5b | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 0.5b | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 0.5b | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
4 calls. Slowest were:
| 9.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 9.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 8.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
4 calls. Slowest were:
| 25.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 24.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 24.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 0.0ms | (sqrt PI) |
103 calls. Slowest were:
| 474.0ms | (* (* (/ 1 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (* (/ 1 2) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 3 4) (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 15 8) (* (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x)))))) |
| 205.0ms | (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) |
| 178.0ms | (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) |
10 alts after pruning (10 fresh and 0 done)
Merged error: 0.6b
Found 4 expressions with local error:
| 1.0b | (sqrt PI) |
| 0.5b | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 0.5b | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 0.4b | (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) |
4 calls. Slowest were:
| 40.0ms | (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) |
| 4.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 4.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
4 calls. Slowest were:
| 31.0ms | (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) |
| 17.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 14.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 0.0ms | (sqrt PI) |
193 calls. Slowest were:
| 556.0ms | (* (* (/ 1 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (* (/ 1 2) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 3 4) (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 15 8) (* (* (* (* (* (pow (fabs x) -2) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x)))))) |
| 458.0ms | (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) |
| 431.0ms | (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x)))) (* (/ 1 (fabs x)) (/ 1 (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) |
11 alts after pruning (10 fresh and 1 done)
Merged error: 0.5b
Found 4 expressions with local error:
| 1.0b | (sqrt PI) |
| 0.5b | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 0.5b | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 0.4b | (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) |
4 calls. Slowest were:
| 54.0ms | (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) |
| 8.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 8.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
4 calls. Slowest were:
| 20.0ms | (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) |
| 20.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 13.0ms | (* (/ 1 (fabs x)) (/ 1 (fabs x))) |
| 0.0ms | (sqrt PI) |
193 calls. Slowest were:
| 502.0ms | (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (* (/ 1 (fabs x)) (/ 1 (fabs x)))) (* (/ 1 (fabs x)) (/ 1 (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) |
| 474.0ms | (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) |
| 401.0ms | (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x)))) |
10 alts after pruning (9 fresh and 1 done)
Merged error: 0.4b
Found 4 expressions with local error:
| 1.0b | (sqrt PI) |
| 0.4b | (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) |
| 0.4b | (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) |
| 0.4b | (* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4)) |
4 calls. Slowest were:
| 62.0ms | (* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4)) |
| 23.0ms | (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) |
| 10.0ms | (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) |
4 calls. Slowest were:
| 77.0ms | (* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4)) |
| 45.0ms | (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) |
| 33.0ms | (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) |
| 0.0ms | (sqrt PI) |
158 calls. Slowest were:
| 3.1s | (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) |
| 2.6s | (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) |
| 644.0ms | (* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4) (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4)) (+ (/ 15/8 (* (fabs x) (fabs x))) 3/4))) |
17 alts after pruning (17 fresh and 0 done)
Merged error: 0.1b
0% (0.5b remaining)
Error of 0.7b against oracle of 0.2b and baseline of 0.7b