Details

sample29.0ms

Algorithm

intervals

Results

12.0ms

267×

body

valid

simplify39.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	19	15
2	36	15
3	48	15
4	66	15
5	72	15
done	72	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: 28.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.0b	(- (* x.im y.re) (* x.re y.im))
28.3b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(- (* x.im y.re) (* x.re y.im))
9.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series50.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
11.0ms	(- (* x.im y.re) (* x.re y.im))
33.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts

64 → 64

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	102	1120
1	289	1097
2	1023	981
3	3795	981
done	5000	980

prune127.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	54	10	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	10	65

Merged error: 28.0b

Counts

65 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* x.im y.re) (* x.re y.im))
18.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

4.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* x.im y.re) (* x.re y.im))
41.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	121	1814
1	304	1682
2	854	1574
3	2504	1558
done	5000	1557

prune149.0ms

Filtered

75 candidates to 98 candidates (-30.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	96	12	108

Merged error: 24.7b

Counts

108 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
1.0b	(- (* x.im y.re) (* x.re y.im))
28.1b	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp` `add-log-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `pow-flip` `diff-log` `sum-log` `inv-pow`

Counts

4 → 138

Calls

4 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
13.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
4.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
11.0ms	(- (* x.im y.re) (* x.re y.im))
20.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify721.0ms

Counts

150 → 150

Iterations

Useful iterations: done (717.0ms)

Iter	Nodes	Cost
0	208	3684
1	515	3430
2	1417	3127
done	5000	3119

prune141.0ms

Filtered

89 candidates to 150 candidates (-68.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	151	11	162

Merged error: 24.7b

Counts

162 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* x.im y.re) (* x.re y.im))
18.6b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

4.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* x.im y.re) (* x.re y.im))
28.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.6s

Counts

97 → 97

Iterations

Useful iterations: 4 (1.8s)

Iter	Nodes	Cost
0	116	1782
1	264	1664
2	703	1562
3	1807	1548
4	4578	1547
done	5001	1547

prune100.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	96	12	108

Merged error: 24.7b

Counts

108 → 12

regimes524.0ms

Accuracy

-11.7% (3.7b remaining)

Error of 27.1b against oracle of 23.3b and baseline of 26.7b

bsearch26.0ms

Steps

Iters	Range		Point
9	-1.3189260295586262e+29	-2.5920945801387674e+23	-1.3042646303164026e+29

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	28	34
2	31	34
3	34	34
done	34	34

end0.0ms

sample823.0ms

Algorithm

intervals

Results

405.0ms

8461×

body

valid

Details

sample29.0ms

simplify39.0ms

prune4.0ms

localize10.0ms

rewrite18.0ms

series50.0ms

simplify1.6s

prune127.0ms

localize14.0ms

rewrite24.0ms

series65.0ms

simplify1.1s

prune149.0ms

localize11.0ms

rewrite36.0ms

series66.0ms

simplify721.0ms

prune141.0ms

localize14.0ms

rewrite25.0ms

series52.0ms

simplify2.6s

prune100.0ms

regimes524.0ms

bsearch26.0ms

simplify5.0ms

end0.0ms

sample823.0ms

Profiling