Details

sample867.0ms

Algorithm

intervals

Results

746.0ms

3363×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	31	103
1	90	103
2	384	66
3	2147	54
done	5000	51

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize46.0ms

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)

rewrite147.0ms

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:

52.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
46.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series120.0ms

Counts

4 → 10

Calls

4 calls:

50.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
43.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify3.1s

Counts

224 → 224

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	146	3221
1	476	2916
2	3423	2553
done	5001	2340

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.5b

localize105.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 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)

rewrite441.0ms

Algorithm

rewrite-expression-head

Rules

241×	`add-exp-log`
145×	`add-cbrt-cube`
114×	`prod-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
85×	`div-exp`
68×	`add-cube-cbrt` `*-un-lft-identity`
66×	`cbrt-unprod`
45×	`cbrt-undiv`
39×	`associate-r`
28×	`pow1`
27×	`associate-l`
26×	`swap-sqr`
19×	`frac-times` `associate-*l/`
9×	`associate-*r/` `div-inv`
8×	`pow-to-exp` `pow-prod-down` `pow-exp` `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 → 247

Calls

4 calls:

301.0ms	(* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
43.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
61.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series142.0ms

Counts

4 → 10

Calls

4 calls:

68.0ms	(* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
37.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
36.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify668.0ms

Counts

257 → 257

Iterations

Useful iterations: done (656.0ms)

Iter	Nodes	Cost
0	276	5427
1	1076	4879
done	5001	3926

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize113.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (/ 1.0 (fabs x)) (/ 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)

rewrite971.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-exp-log` `add-cbrt-cube`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
62×	`pow-plus` `pow-prod-up`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
12×	`pow-prod-down`
10×	`pow2` `pow-sqr`
9×	`div-inv`
8×	`unswap-sqr`
4×	`pow3` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 332

Calls

4 calls:

834.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
38.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
50.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(sqrt PI)

series180.0ms

Counts

4 → 10

Calls

4 calls:

88.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
46.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
46.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify1.1s

Counts

342 → 342

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	393	8642
1	1615	7035
done	5000	4920

prune2.7s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (/ 1.0 (fabs x)) (/ 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)

rewrite955.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-exp-log` `add-cbrt-cube`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
62×	`pow-plus` `pow-prod-up`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
12×	`pow-prod-down`
10×	`pow2` `pow-sqr`
9×	`div-inv`
8×	`unswap-sqr`
4×	`pow3` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 332

Calls

4 calls:

840.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
56.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series173.0ms

Counts

4 → 10

Calls

4 calls:

90.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
47.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
35.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify1.0s

Counts

342 → 342

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	368	8554
1	1468	7518
done	5001	4510

prune2.0s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

regimes471.0ms

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	94
1	53	94
done	53	94

end0.0ms

sample2.4s

Algorithm

intervals

Results

2.2s

7630×

body

valid