Details

sample69.0ms

Algorithm

intervals

Results

17.0ms	193×	body	80	valid
10.0ms	18×	body	2560	valid
8.0ms	19×	body	1280	valid
4.0ms	7×	body	5120	valid
3.0ms	9×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	24
2	24
1	22
0	12

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `sqrt-prod` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `sum-log` `pow1/2` `associate-*r/`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

6.0ms	(+ (* re re) (* im im))
23.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
23.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
9.0ms	(sqrt (+ (* re re) (* im im)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* re re) (* im im))
245.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
52.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms	(sqrt (+ (* re re) (* im im)))

simplify700.0ms

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
2	1360
1	291
0	108

prune430.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (pow im 2) (* re re)))) (sqrt (sqrt (+ (pow im 2) (* re re)))))
8.4b	(+ (* (sqrt (sqrt (+ (pow im 2) (* re re)))) (sqrt (sqrt (+ (pow im 2) (* re re))))) re)
28.4b	(sqrt (+ (pow im 2) (* re re)))
28.4b	(sqrt (+ (pow im 2) (* re re)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

69.0ms	(* (sqrt (sqrt (+ (pow im 2) (* re re)))) (sqrt (sqrt (+ (pow im 2) (* re re)))))
33.0ms	(+ (* (sqrt (sqrt (+ (pow im 2) (* re re)))) (sqrt (sqrt (+ (pow im 2) (* re re))))) re)
13.0ms	(sqrt (+ (pow im 2) (* re re)))
21.0ms	(sqrt (+ (pow im 2) (* re re)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sqrt (sqrt (+ (pow im 2) (* re re)))) (sqrt (sqrt (+ (pow im 2) (* re re)))))
76.0ms	(+ (* (sqrt (sqrt (+ (pow im 2) (* re re)))) (sqrt (sqrt (+ (pow im 2) (* re re))))) re)
60.0ms	(sqrt (+ (pow im 2) (* re re)))
48.0ms	(sqrt (+ (pow im 2) (* re re)))

simplify809.0ms

Counts

136 → 136

Iterations

Iter	Nodes
done	5001
2	1161
1	298
0	133

prune603.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (sqrt (sqrt (sqrt (+ (pow im 2) (* re re))))) 3)
12.0b	(+ (* (sqrt (sqrt (sqrt (+ (pow im 2) (* re re))))) (pow (sqrt (sqrt (sqrt (+ (pow im 2) (* re re))))) 3)) re)
28.4b	(sqrt (+ (pow im 2) (* re re)))
28.4b	(sqrt (+ (pow im 2) (* re re)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod`
11×	`sqrt-pow1`
10×	`pow1` `sqrt-div`
7×	`pow-pow`
6×	`add-log-exp`
5×	`add-cbrt-cube` `pow1/2` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`pow-unpow`
2×	`cube-div` `rem-sqrt-square`
1×	`cube-mult` `pow-to-exp` `+-commutative` `sum-log` `unpow3` `pow-exp` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

32.0ms	(pow (sqrt (sqrt (sqrt (+ (pow im 2) (* re re))))) 3)
72.0ms	(+ (* (sqrt (sqrt (sqrt (+ (pow im 2) (* re re))))) (pow (sqrt (sqrt (sqrt (+ (pow im 2) (* re re))))) 3)) re)
21.0ms	(sqrt (+ (pow im 2) (* re re)))
21.0ms	(sqrt (+ (pow im 2) (* re re)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow (sqrt (sqrt (sqrt (+ (pow im 2) (* re re))))) 3)
66.0ms	(+ (* (sqrt (sqrt (sqrt (+ (pow im 2) (* re re))))) (pow (sqrt (sqrt (sqrt (+ (pow im 2) (* re re))))) 3)) re)
50.0ms	(sqrt (+ (pow im 2) (* re re)))
45.0ms	(sqrt (+ (pow im 2) (* re re)))

simplify1.0s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
2	1609
1	479
0	151

prune612.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 10.4b

localize109.0ms

Local error

Found 4 expressions with local error:

28.4b	(sqrt (+ (pow im 2) (* re re)))
28.4b	(sqrt (+ (pow im 2) (* re re)))
28.4b	(sqrt (+ (pow im 2) (* re re)))
28.4b	(sqrt (+ (pow im 2) (* re re)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

15.0ms	(sqrt (+ (pow im 2) (* re re)))
22.0ms	(sqrt (+ (pow im 2) (* re re)))
24.0ms	(sqrt (+ (pow im 2) (* re re)))
22.0ms	(sqrt (+ (pow im 2) (* re re)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (+ (pow im 2) (* re re)))
47.0ms	(sqrt (+ (pow im 2) (* re re)))
56.0ms	(sqrt (+ (pow im 2) (* re re)))
52.0ms	(sqrt (+ (pow im 2) (* re re)))

simplify581.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	935
2	247
1	85
0	38

prune811.0ms

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 10.4b

regimes1.3s

Accuracy

51.6% (13.9b remaining)

Error of 23.5b against oracle of 9.7b and baseline of 38.4b

bsearch377.0ms

Steps

Iters	Range		Point
9	3.0455316621450604e+53	6.601528886642014e+60	1.605778950101428e+60
11	2.614178172688935e-120	9.328905982034919e-98	1.1456858364248567e-118
8	-2.986264416976082e-65	-6.704894791063431e-68	-6.768391877498059e-68
5	-3.50290590301885e+78	-1.723051907656132e+78	-3.1150436889321725e+78

simplify15.0ms

Iterations

Iter	Nodes
done	65
2	65
1	63
0	47

end0.0ms

sample2.2s

Algorithm

intervals

Results

937.0ms	6031×	body	80	valid
416.0ms	695×	body	2560	valid
222.0ms	447×	body	1280	valid
208.0ms	300×	body	5120	valid
79.0ms	293×	body	640	valid
30.0ms	151×	body	320	valid
10.0ms	83×	body	160	valid