Details

sample29.0ms

Algorithm

intervals

Results

13.0ms

267×

body

valid

simplify36.0ms

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)))

series48.0ms

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))
31.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify822.0ms

Counts

64 → 64

Iterations

Useful iterations: done (820.0ms)

Iter	Nodes	Cost
0	102	1120
1	289	1097
2	1076	981
3	3379	981
done	5000	980

prune136.0ms

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)))

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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* x.im y.re) (* x.re y.im))
40.0ms	(/ (- (* 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)))

simplify734.0ms

Counts

98 → 98

Iterations

Useful iterations: done (731.0ms)

Iter	Nodes	Cost
0	121	1814
1	311	1690
2	918	1574
3	2754	1558
done	5000	1557

prune147.0ms

Filtered

76 candidates to 98 candidates (-28.9%)

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)))

rewrite33.0ms

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
30.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (- (* x.im y.re) (* x.re y.im))))
15.0ms	(- (* 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)))

simplify454.0ms

Counts

150 → 150

Iterations

Useful iterations: done (449.0ms)

Iter	Nodes	Cost
0	208	3684
1	524	3478
2	1854	3127
done	5000	3119

prune143.0ms

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

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)))

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` `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)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* x.im y.re) (* x.re y.im))
31.0ms	(/ (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)))

simplify1.3s

Counts

97 → 97

Iterations

Useful iterations: 4 (625.0ms)

Iter	Nodes	Cost
0	116	1782
1	271	1664
2	725	1562
3	1886	1548
4	4803	1547
done	5000	1547

prune100.0ms

Filtered

73 candidates to 97 candidates (-32.9%)

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

regimes362.0ms

Accuracy

-11.7% (3.7b remaining)

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

bsearch23.0ms

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

sample843.0ms

Algorithm

intervals

Results

414.0ms

8461×

body

valid

Details

sample29.0ms

simplify36.0ms

prune4.0ms

localize10.0ms

rewrite18.0ms

series48.0ms

simplify822.0ms

prune136.0ms

localize14.0ms

rewrite25.0ms

series67.0ms

simplify734.0ms

prune147.0ms

localize12.0ms

rewrite33.0ms

series71.0ms

simplify454.0ms

prune143.0ms

localize14.0ms

rewrite24.0ms

series55.0ms

simplify1.3s

prune100.0ms

regimes362.0ms

bsearch23.0ms

simplify4.0ms

end0.0ms

sample843.0ms

Profiling