Details

sample321.0ms

Algorithm

intervals

Results

253.0ms

3254×

body

valid

simplify66.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36
done	5001	36

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 214

Calls

4 calls:

22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series77.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify70.0ms

Counts

224 → 224

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	426	1780
1	2077	1524
2	5002	1377
done	5002	1377

prune994.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (* 1 (/ (* 1.0 1.0) (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

2109×	`add-exp-log`
1322×	`prod-exp`
697×	`div-exp`
637×	`add-cbrt-cube`
362×	`cbrt-unprod`
185×	`cbrt-undiv`
112×	`1-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
64×	`pow-to-exp` `pow-exp`
51×	`frac-times` `associate-*l/`
39×	`pow1` `associate-r`
33×	`associate-*r/`
27×	`associate-l`
26×	`swap-sqr`
17×	`pow-prod-down`
9×	`div-inv`
8×	`unswap-sqr`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 537

Calls

4 calls:

3.1s	(* (* (* (* (* 1 (/ (* 1.0 1.0) (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series106.0ms

Counts

4 → 10

Calls

4 calls:

57.0ms	(* (* (* (* (* 1 (/ (* 1.0 1.0) (pow (fabs x) 2))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify111.0ms

Counts

547 → 547

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	3019	9555
1	5002	6683
done	5002	6683

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
90×	`times-frac`
69×	`add-exp-log` `add-cbrt-cube`
68×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
38×	`pow1`
27×	`associate-l`
26×	`swap-sqr` `prod-exp` `cbrt-unprod`
21×	`cbrt-undiv` `div-exp`
10×	`unswap-sqr`
9×	`div-inv`
8×	`pow-plus` `pow-prod-up`
7×	`frac-times` `associate-*l/`
5×	`associate-*r/` `pow-prod-down`
4×	`pow2` `pow-sqr` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow3`

Counts

4 → 209

Calls

4 calls:

45.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
21.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series89.0ms

Counts

4 → 10

Calls

4 calls:

36.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
28.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify76.0ms

Counts

219 → 219

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	524	1755
1	2745	1311
2	5002	1183
done	5002	1183

prune967.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
90×	`times-frac`
69×	`add-exp-log` `add-cbrt-cube`
68×	`add-cube-cbrt` `*-un-lft-identity`
39×	`associate-r`
38×	`pow1`
27×	`associate-l`
26×	`swap-sqr` `prod-exp` `cbrt-unprod`
21×	`cbrt-undiv` `div-exp`
10×	`unswap-sqr`
9×	`div-inv`
8×	`pow-plus` `pow-prod-up`
7×	`frac-times` `associate-*l/`
5×	`associate-*r/` `pow-prod-down`
4×	`pow2` `pow-sqr` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow3`

Counts

4 → 209

Calls

4 calls:

44.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series85.0ms

Counts

4 → 10

Calls

4 calls:

36.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify95.0ms

Counts

219 → 219

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	608	1807
1	3189	1360
2	5002	1250
done	5002	1250

prune1.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

regimes237.0ms

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	47
1	45	47
done	45	47

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

17495×

body

valid