Details

sample35.0ms

Algorithm

intervals

Results

17.0ms

267×

body

valid

simplify31.0ms

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)))

rewrite21.0ms

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))
12.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series47.0ms

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))
30.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify968.0ms

Counts

64 → 64

Iterations

Useful iterations: done (966.0ms)

Iter	Nodes	Cost
0	102	1120
1	289	1097
2	1143	983
3	3679	981
done	5000	980

prune139.0ms

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

localize17.0ms

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)))

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` `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)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* x.im y.re) (* x.re y.im))
39.0ms	(/ (- (* 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)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify775.0ms

Counts

98 → 98

Iterations

Useful iterations: done (769.0ms)

Iter	Nodes	Cost
0	121	1814
1	311	1691
2	936	1577
3	2920	1558
done	5000	1557

prune156.0ms

Filtered

78 candidates to 98 candidates (-25.6%)

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

localize12.0ms

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)))

rewrite34.0ms

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:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(/ 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)))

series70.0ms

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))
24.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im)))

simplify839.0ms

Counts

150 → 150

Iterations

Useful iterations: done (834.0ms)

Iter	Nodes	Cost
0	208	3684
1	524	3488
2	1955	3196
done	5000	3119

prune183.0ms

Filtered

88 candidates to 150 candidates (-70.5%)

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

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* y.re x.im) (* y.im x.re))
18.6b	(/ (sqrt (+ (pow y.re 2) (pow y.im 2))) (- (* y.re x.im) (* y.im x.re)))
29.4b	(sqrt (+ (pow y.re 2) (pow y.im 2)))
29.4b	(sqrt (+ (pow y.re 2) (pow y.im 2)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
30×	`sqrt-prod`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
12×	`unpow-prod-down` `distribute-lft-out`
8×	`associate-/l*`
6×	`pow1` `add-exp-log` `sqrt-div` `add-cbrt-cube` `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 → 97

Calls

4 calls:

4.0ms	(- (* y.re x.im) (* y.im x.re))
17.0ms	(/ (sqrt (+ (pow y.re 2) (pow y.im 2))) (- (* y.re x.im) (* y.im x.re)))
8.0ms	(sqrt (+ (pow y.re 2) (pow y.im 2)))
9.0ms	(sqrt (+ (pow y.re 2) (pow y.im 2)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* y.re x.im) (* y.im x.re))
27.0ms	(/ (sqrt (+ (pow y.re 2) (pow y.im 2))) (- (* y.re x.im) (* y.im x.re)))
7.0ms	(sqrt (+ (pow y.re 2) (pow y.im 2)))
7.0ms	(sqrt (+ (pow y.re 2) (pow y.im 2)))

simplify645.0ms

Counts

109 → 109

Iterations

Useful iterations: done (636.0ms)

Iter	Nodes	Cost
0	118	2034
1	268	1865
2	834	1787
3	2177	1776
done	5000	1775

prune270.0ms

Filtered

74 candidates to 109 candidates (-47.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	108	12	120

Merged error: 24.7b

Counts

120 → 12

regimes396.0ms

Accuracy

-11.7% (3.7b remaining)

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

bsearch24.0ms

Steps

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

simplify4.0ms

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

sample868.0ms

Algorithm

intervals

Results

435.0ms

8461×

body

valid

Details

sample35.0ms

simplify31.0ms

prune4.0ms

localize10.0ms

rewrite21.0ms

series47.0ms

simplify968.0ms

prune139.0ms

localize17.0ms

rewrite25.0ms

series63.0ms

simplify775.0ms

prune156.0ms

localize12.0ms

rewrite34.0ms

series70.0ms

simplify839.0ms

prune183.0ms

localize15.0ms

rewrite41.0ms

series52.0ms

simplify645.0ms

prune270.0ms

regimes396.0ms

bsearch24.0ms

simplify4.0ms

end0.0ms

sample868.0ms

Profiling