Details

sample45.0ms

Algorithm

intervals

Results

12.0ms	24×	body	2560	valid
11.0ms	197×	body	80	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

prune4.0ms

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

series44.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify622.0ms

Counts

49 → 49

Iterations

Useful iterations: 3 (202.0ms)

Iter	Nodes	Cost
0	98	728
1	245	633
2	747	581
3	2087	560
done	5001	560

prune123.0ms

Filtered

41 candidates to 49 candidates (-19.5%)

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

localize15.0ms

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)))

rewrite48.0ms

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)))
19.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
5.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(sqrt (+ (* re re) (* im im)))

series49.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify670.0ms

Counts

66 → 66

Iterations

Useful iterations: 3 (223.0ms)

Iter	Nodes	Cost
0	101	1327
1	258	845
2	782	737
3	2288	730
done	5000	730

prune125.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

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)))

series29.0ms

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)))

simplify993.0ms

Counts

75 → 75

Iterations

Useful iterations: 4 (409.0ms)

Iter	Nodes	Cost
0	101	1226
1	211	1050
2	490	756
3	1265	730
4	3050	724
done	5000	724

prune155.0ms

Filtered

64 candidates to 75 candidates (-17.2%)

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

localize22.0ms

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:

7.0ms	(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)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(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)))
14.0ms	(log (+ (* re re) (* im im)))

simplify694.0ms

Counts

78 → 78

Iterations

Useful iterations: 3 (243.0ms)

Iter	Nodes	Cost
0	141	1465
1	333	1370
2	882	1169
3	2356	1141
done	5000	1141

prune187.0ms

Filtered

68 candidates to 78 candidates (-14.7%)

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

regimes331.0ms

Accuracy

59% (9.6b remaining)

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

bsearch65.0ms

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

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	47	106
1	61	104
2	65	104
done	65	104

end0.0ms

sample1.2s

Algorithm

intervals

Results

341.0ms	6013×	body	80	valid
229.0ms	717×	body	2560	valid
129.0ms	493×	body	1280	valid
119.0ms	296×	body	5120	valid
57.0ms	274×	body	640	valid
22.0ms	125×	body	320	valid
9.0ms	82×	body	160	valid

Details

sample45.0ms

simplify8.0ms

prune4.0ms

localize11.0ms

rewrite22.0ms

series44.0ms

simplify622.0ms

prune123.0ms

localize15.0ms

rewrite48.0ms

series49.0ms

simplify670.0ms

prune125.0ms

localize19.0ms

rewrite37.0ms

series29.0ms

simplify993.0ms

prune155.0ms

localize22.0ms

rewrite35.0ms

series97.0ms

simplify694.0ms

prune187.0ms

regimes331.0ms

bsearch65.0ms

simplify7.0ms

end0.0ms

sample1.2s

Profiling