Details

sample861.0ms

Algorithm

intervals

Results

739.0ms

3603×

body

valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	2303
2	401
1	90
0	31

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize138.0ms

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)

rewrite121.0ms

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:

32.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series124.0ms

Counts

4 → 10

Calls

4 calls:

52.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
43.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify2.6s

Counts

232 → 232

Iterations

Iter	Nodes
done	5001
2	3376
1	480
0	150

prune2.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.4b

localize110.0ms

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

rewrite739.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-cbrt-cube` `add-exp-log`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`*-un-lft-identity` `add-cube-cbrt`
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×	`expm1-log1p-u` `pow3` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 340

Calls

4 calls:

656.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
18.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
33.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series174.0ms

Counts

4 → 10

Calls

4 calls:

80.0ms	(* (* (* (* (/ 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)))
47.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify2.0s

Counts

350 → 350

Iterations

Iter	Nodes
done	5001
1	1485
0	374

prune2.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.4b

localize150.0ms

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	(expm1 (log1p (sqrt PI)))
1.0b	(sqrt PI)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 164

Calls

4 calls:

17.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(expm1 (log1p (sqrt PI)))
1.0ms	(sqrt PI)

series91.0ms

Counts

4 → 8

Calls

4 calls:

46.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
44.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(expm1 (log1p (sqrt PI)))
0.0ms	(sqrt PI)

simplify1.9s

Counts

172 → 172

Iterations

Iter	Nodes
done	5000
2	2787
1	418
0	139

prune2.1s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 0.3b

localize176.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (/ (* 1.0 1.0) (* (fabs x) (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)
1.0b	(expm1 (log1p (sqrt PI)))

rewrite536.0ms

Algorithm

rewrite-expression-head

Rules

321×	`add-cbrt-cube` `add-exp-log`
166×	`prod-exp` `cbrt-unprod`
101×	`cbrt-undiv` `div-exp`
53×	`add-sqr-sqrt` `times-frac`
40×	`*-un-lft-identity` `add-cube-cbrt`
26×	`associate-r`
25×	`pow1`
18×	`frac-times` `associate-*l/`
14×	`associate-l`
13×	`swap-sqr`
8×	`associate-*r/`
7×	`pow-prod-down`
5×	`pow-plus` `pow-prod-up` `div-inv`
4×	`expm1-log1p-u` `pow3` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`*-commutative`
1×	`pow2` `rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow1/2` `pow-sqr` `expm1-udef`

Counts

4 → 233

Calls

4 calls:

473.0ms	(* (* (* (/ (* 1.0 1.0) (* (fabs x) (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
30.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)
0.0ms	(expm1 (log1p (sqrt PI)))

series120.0ms

Counts

4 → 8

Calls

4 calls:

82.0ms	(* (* (* (/ (* 1.0 1.0) (* (fabs x) (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
38.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)
0.0ms	(expm1 (log1p (sqrt PI)))

simplify1.5s

Counts

241 → 241

Iterations

Iter	Nodes
done	5001
1	1553
0	379

prune2.0s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 0.3b

regimes695.0ms

bsearch0.0ms

simplify28.0ms

Iterations

Iter	Nodes
done	62
1	62
0	43

end0.0ms

sample2.6s

Algorithm

intervals

Results

2.3s

8764×

body

valid