Details

sample786.0ms

Algorithm

intervals

Results

696.0ms

3624×

body

valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	31	958
1	90	918
2	401	843
3	2303	829
done	5001	763

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize83.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
120×	`times-frac`
89×	`*-un-lft-identity` `add-cube-cbrt`
40×	`add-cbrt-cube` `add-exp-log`
39×	`swap-sqr` `associate-r` `associate-l`
26×	`pow1`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 222

Calls

4 calls:

34.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
31.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series134.0ms

Counts

4 → 10

Calls

4 calls:

44.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
49.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
42.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify2.7s

Counts

232 → 232

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	144	57257
1	435	51246
2	2805	49437
done	5000	47157

prune2.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.4b

localize98.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
120×	`times-frac`
89×	`*-un-lft-identity` `add-cube-cbrt`
40×	`add-cbrt-cube` `add-exp-log`
39×	`swap-sqr` `associate-r` `associate-l`
26×	`pow1`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 222

Calls

4 calls:

39.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
19.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series95.0ms

Counts

4 → 10

Calls

4 calls:

26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
38.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
30.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify2.5s

Counts

232 → 232

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	146	57297
1	443	51286
2	3012	49357
done	5000	47197

prune2.3s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 0.3b

localize90.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (* (fabs x) (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-cbrt-cube` `add-exp-log`
90×	`add-sqr-sqrt`
84×	`times-frac`
63×	`*-un-lft-identity` `add-cube-cbrt`
40×	`prod-exp` `cbrt-unprod`
33×	`associate-l`
30×	`cbrt-undiv` `div-exp`
27×	`associate-r`
26×	`swap-sqr`
24×	`pow1`
10×	`unswap-sqr`
9×	`div-inv`
7×	`frac-times` `associate-*r/`
5×	`pow-prod-down` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sqrt-prod`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 212

Calls

4 calls:

83.0ms	(* (/ 1.0 (* (fabs x) (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
35.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
46.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series153.0ms

Counts

4 → 10

Calls

4 calls:

77.0ms	(* (/ 1.0 (* (fabs x) (fabs x))) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))))
47.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
28.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify1.3s

Counts

222 → 222

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	202	61399
1	711	53295
done	5001	50568

prune2.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.2b

localize104.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
80×	`times-frac`
62×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 168

Calls

4 calls:

31.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
20.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series59.0ms

Counts

4 → 8

Calls

4 calls:

29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
30.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify2.1s

Counts

176 → 176

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	128	40116
1	402	35894
2	2664	34688
done	5000	33168

prune1.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.1b

regimes870.0ms

bsearch0.0ms

simplify17.0ms

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	28	883
1	31	883
done	31	883

end0.0ms

sample5.6s

Algorithm

intervals

Results

5.2s

19409×

body

valid