Details

sample860.0ms

Algorithm

intervals

Results

754.0ms

3337×

body

valid

simplify3.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1913
2	396
1	90
0	31

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize164.0ms

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)

rewrite100.0ms

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:

17.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
29.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
35.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(sqrt PI)

series114.0ms

Counts

4 → 10

Calls

4 calls:

39.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
38.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify2.2s

Counts

232 → 232

Iterations

Iter	Nodes
done	5000
2	1531
1	469
0	150

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.4b

localize119.0ms

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)

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
90×	`times-frac`
69×	`add-cbrt-cube` `add-exp-log`
68×	`*-un-lft-identity` `add-cube-cbrt`
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×	`pow-prod-down` `associate-*r/`
4×	`pow2` `expm1-log1p-u` `pow-sqr` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow3`

Counts

4 → 217

Calls

4 calls:

70.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
33.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
34.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series165.0ms

Counts

4 → 10

Calls

4 calls:

74.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
45.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
46.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify2.9s

Counts

227 → 227

Iterations

Iter	Nodes
done	5001
2	2297
1	665
0	205

prune2.3s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.3b

localize134.0ms

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

rewrite87.0ms

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:

37.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
36.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(expm1 (log1p (sqrt PI)))
2.0ms	(sqrt PI)

series90.0ms

Counts

4 → 8

Calls

4 calls:

44.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
45.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(expm1 (log1p (sqrt PI)))
0.0ms	(sqrt PI)

simplify3.0s

Counts

172 → 172

Iterations

Iter	Nodes
done	5112
3	4117
2	1337
1	407
0	139

prune2.1s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.2b

localize145.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(expm1 (log1p (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`pow1` `swap-sqr` `associate-r` `associate-l`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `expm1-log1p` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `expm1-udef`

Counts

4 → 110

Calls

4 calls:

22.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
0.0ms	(expm1 (log1p (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))))

series38.0ms

Counts

4 → 6

Calls

4 calls:

37.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(expm1 (log1p (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))))

simplify3.0s

Counts

116 → 116

Iterations

Iter	Nodes
done	5102
3	4309
2	1351
1	416
0	141

prune1.4s

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 0.2b

regimes474.0ms

bsearch0.0ms

simplify21.0ms

Iterations

Iter	Nodes
done	51
1	51
0	35

end0.0ms

sample4.0s

Algorithm

intervals

Results

3.8s

13294×

body

valid