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

prune9.0ms

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

localize11.0ms

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)))

rewrite22.0ms

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:

9.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series42.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify850.0ms

Counts

49 → 49

Iterations

Useful iterations: done (843.0ms)

Iter	Nodes	Cost
0	98	728
1	245	627
2	708	581
3	1909	560
done	5001	555

prune113.0ms

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)))

rewrite43.0ms

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:

17.0ms	(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)
4.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt (* 2.0 (+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)))
11.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify665.0ms

Counts

66 → 66

Iterations

Useful iterations: 3 (225.0ms)

Iter	Nodes	Cost
0	101	1327
1	258	793
2	768	737
3	2172	714
done	5000	714

prune123.0ms

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

localize19.0ms

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)))

rewrite37.0ms

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)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (exp (log (sqrt (+ (* re re) (* im im))))))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify953.0ms

Counts

75 → 75

Iterations

Useful iterations: 4 (363.0ms)

Iter	Nodes	Cost
0	101	1226
1	211	1040
2	440	730
3	1017	724
4	2620	708
done	5000	708

prune143.0ms

Filtered

59 candidates to 75 candidates (-27.1%)

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

localize21.0ms

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)))

rewrite35.0ms

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:

8.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
17.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(log (+ (* re re) (* im im)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (exp 1/2) (log (+ (* re re) (* im im))))
49.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (pow (exp 1/2) (log (+ (* re re) (* im im)))))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))
13.0ms	(log (+ (* re re) (* im im)))

simplify698.0ms

Counts

78 → 78

Iterations

Useful iterations: 3 (252.0ms)

Iter	Nodes	Cost
0	141	1465
1	333	1368
2	839	1167
3	2313	1139
done	5000	1139

prune181.0ms

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

regimes312.0ms

Accuracy

59% (9.6b remaining)

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

bsearch62.0ms

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

319.0ms	6013×	body	80	valid
217.0ms	717×	body	2560	valid
126.0ms	493×	body	1280	valid
106.0ms	296×	body	5120	valid
57.0ms	274×	body	640	valid
18.0ms	125×	body	320	valid
8.0ms	82×	body	160	valid

Details

sample38.0ms

simplify8.0ms

prune9.0ms

localize11.0ms

rewrite22.0ms

series42.0ms

simplify850.0ms

prune113.0ms

localize14.0ms

rewrite43.0ms

series52.0ms

simplify665.0ms

prune123.0ms

localize19.0ms

rewrite37.0ms

series28.0ms

simplify953.0ms

prune143.0ms

localize21.0ms

rewrite35.0ms

series96.0ms

simplify698.0ms

prune181.0ms

regimes312.0ms

bsearch62.0ms

simplify5.0ms

end0.0ms

sample1.1s

Profiling