Details

sample38.0ms

Algorithm

intervals

Results

10.0ms	197×	body	80	valid
7.0ms	24×	body	2560	valid
4.0ms	15×	body	1280	valid
3.0ms	7×	body	5120	valid
2.0ms	8×	body	640	valid
0.0ms	2×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	15
1	22	15
2	23	15
done	23	15

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 38.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.5b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.6b	(+ (sqrt (+ (* re re) (* im im))) re)
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
6×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`add-cube-cbrt` `sqrt-div` `sqrt-prod`
3×	`add-exp-log` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `distribute-lft-out`

Counts

3 → 40

Calls

3 calls:

8.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series45.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
12.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.0s

Counts

49 → 49

Iterations

Useful iterations: 3 (329.0ms)

Iter	Nodes	Cost
0	98	728
1	243	627
2	692	581
3	2153	560
done	5001	560

prune111.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	42	7	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 18.0b

Counts

50 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (* 2.0 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
6.4b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
29.8b	(sqrt (+ (* re re) (* im im)))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div` `add-log-exp`
4×	`add-exp-log` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`pow1/2`
2×	`rem-sqrt-square` `associate-*r/`
1×	`+-commutative` `pow-prod-down` `sum-log`

Counts

4 → 54

Calls

4 calls:

16.0ms	(sqrt (* 2.0 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
16.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
8.0ms	(sqrt (+ (* re re) (* im im)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (* 2.0 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
8.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.1s

Counts

66 → 66

Iterations

Useful iterations: 3 (340.0ms)

Iter	Nodes	Cost
0	101	1327
1	256	793
2	751	737
3	2416	714
done	5001	714

prune120.0ms

Filtered

56 candidates to 66 candidates (-17.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	66	7	73

Merged error: 18.0b

Counts

73 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

5.7b	(exp (log (sqrt (+ (* re re) (* im im)))))
14.0b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
29.8b	(sqrt (+ (* re re) (* im im)))
29.8b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
8×	`pow1`
6×	`log-prod` `exp-prod` `sqrt-div` `exp-sum` `add-log-exp`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1` `pow1/2` `log-pow`
2×	`rem-sqrt-square` `log-div` `exp-diff`
1×	`+-commutative` `sum-log` `rem-exp-log`

Counts

4 → 63

Calls

4 calls:

7.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
19.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
9.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts

75 → 75

Iterations

Useful iterations: 4 (519.0ms)

Iter	Nodes	Cost
0	101	1226
1	209	1040
2	428	730
3	986	724
4	2531	708
done	5000	708

prune139.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	74	8	82

Merged error: 18.0b

Counts

82 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

6.2b	(pow (exp 1/2) (log (+ (* re re) (* im im))))
14.2b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
29.8b	(sqrt (+ (* re re) (* im im)))
31.0b	(log (+ (* re re) (* im im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`log-prod` `add-log-exp`
5×	`add-exp-log`
4×	`log-div` `pow-unpow` `pow-pow` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`unpow-prod-up` `unpow-prod-down` `exp-prod` `sqrt-prod`
2×	`sqrt-div` `log-pow` `pow-sub`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-exp` `sum-log` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

7.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
16.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(log (+ (* re re) (* im im)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
46.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
13.0ms	(log (+ (* re re) (* im im)))

simplify1.1s

Counts

78 → 78

Iterations

Useful iterations: 3 (415.0ms)

Iter	Nodes	Cost
0	141	1465
1	329	1368
2	789	1167
3	2038	1139
done	5001	1139

prune173.0ms

Filtered

66 candidates to 78 candidates (-18.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	77	9	86

Merged error: 18.0b

Counts

86 → 9

regimes300.0ms

Accuracy

59% (9.6b remaining)

Error of 26.9b against oracle of 17.3b and baseline of 40.6b

bsearch59.0ms

Steps

Iters	Range	Point
9	3.43401543638109e+114	5.025550553073085e+120	7.069821228227976e+116
10	1.3994626587696508e-214	2.9831774035161146e-199	4.1753668252846765e-213
6	-3.9639939611996993e-296	-2.6703687768748694e-297	-1.613340222761899e-296

Iters

Range

Point

3.43401543638109e+114

5.025550553073085e+120

7.069821228227976e+116

1.3994626587696508e-214

2.9831774035161146e-199

4.1753668252846765e-213

-3.9639939611996993e-296

-2.6703687768748694e-297

-1.613340222761899e-296

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	47	106
1	61	104
done	61	104

end0.0ms

sample1.1s

Algorithm

intervals

Results

321.0ms	6013×	body	80	valid
207.0ms	717×	body	2560	valid
123.0ms	493×	body	1280	valid
102.0ms	296×	body	5120	valid
52.0ms	274×	body	640	valid
18.0ms	125×	body	320	valid
8.0ms	82×	body	160	valid

Details

sample38.0ms

simplify8.0ms

prune3.0ms

localize10.0ms

rewrite21.0ms

series45.0ms

simplify1.0s

prune111.0ms

localize14.0ms

rewrite46.0ms

series47.0ms

simplify1.1s

prune120.0ms

localize17.0ms

rewrite36.0ms

series30.0ms

simplify1.4s

prune139.0ms

localize20.0ms

rewrite34.0ms

series90.0ms

simplify1.1s

prune173.0ms

regimes300.0ms

bsearch59.0ms

simplify5.0ms

end0.0ms

sample1.1s

Profiling