Details

sample842.0ms

Algorithm

intervals

Results

713.0ms

3612×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	31	103
1	90	103
2	401	65
3	2320	51
done	5000	49

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 222

Calls

4 calls:

26.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
38.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
42.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(sqrt PI)

series105.0ms

Counts

4 → 10

Calls

4 calls:

28.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
31.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
45.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify3.2s

Counts

232 → 232

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	150	3287
1	480	2982
2	3432	2630
done	5000	2463

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.4b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

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` `expm1-log1p-u` `pow-sqr` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow3`

Counts

4 → 217

Calls

4 calls:

72.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
56.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
45.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
3.0ms	(sqrt PI)

series132.0ms

Counts

4 → 10

Calls

4 calls:

66.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
30.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
36.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify607.0ms

Counts

227 → 227

Iterations

Useful iterations: done (600.0ms)

Iter	Nodes	Cost
0	179	3376
1	612	2997
done	5000	2392

prune2.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.4b

localize101.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

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` `expm1-log1p-u` `pow-sqr` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow3`

Counts

4 → 217

Calls

4 calls:

54.0ms	(* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
39.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
25.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms	(sqrt PI)

series146.0ms

Counts

4 → 10

Calls

4 calls:

54.0ms	(* (* (/ 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)

simplify550.0ms

Counts

227 → 227

Iterations

Useful iterations: done (531.0ms)

Iter	Nodes	Cost
0	179	3376
1	612	2997
done	5000	2392

prune2.0s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.4b

localize95.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
80×	`times-frac`
61×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
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` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow1/2` `expm1-udef`

Counts

4 → 164

Calls

4 calls:

49.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
46.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(expm1 (log1p (sqrt PI)))
3.0ms	(sqrt PI)

series93.0ms

Counts

4 → 8

Calls

4 calls:

46.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
47.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(expm1 (log1p (sqrt PI)))
0.0ms	(sqrt PI)

simplify2.3s

Counts

172 → 172

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	139	2212
1	418	1978
2	2763	1762
done	5000	1622

prune1.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.3b

regimes494.0ms

bsearch0.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	37	100
1	53	100
done	53	100

end0.0ms

sample13.3s

Algorithm

intervals

Results

12.1s

44659×

body

valid