Details

analyze330.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

sample29.0ms

Algorithm

intervals

Results

10.0ms	213×	body	80	valid
4.0ms	14×	body	2560	valid
3.0ms	13×	body	1280	valid
2.0ms	6×	body	5120	valid
1.0ms	8×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 33.5b

Counts

2 → 1

localize11.0ms

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)))
0.2b	(+ (sqrt (+ (* re re) (* im im))) re)
26.8b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

7.0ms	(+ (* re re) (* im im))
8.0ms	(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

4 → 12

Calls

4 calls:

6.0ms	(+ (* re re) (* im im))
25.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify32.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5008	690

prune122.0ms

Filtered

53 candidates to 63 candidates (-18.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	7	64

Merged error: 13.8b

Counts

64 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
5.1b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
26.8b	(sqrt (+ (* re re) (* im im)))
26.8b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

16.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
18.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(sqrt (+ (* re re) (* im im)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.0ms	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify74.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune138.0ms

Filtered

72 candidates to 136 candidates (-88.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 13.8b

Counts

143 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (sqrt (+ (* re re) (* im im))) re)
3.8b	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
23.8b	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
26.8b	(sqrt (+ (* re re) (* im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
7×	`add-cube-cbrt` `sqrt-prod`
6×	`times-frac` `associate-/r*` `add-log-exp` `difference-of-squares`
3×	`sqrt-pow1` `sqrt-div` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `pow1/2` `div-exp` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `flip3-+` `diff-log` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
11.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
5.0ms	(sqrt (+ (* re re) (* im im)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (sqrt (+ (* re re) (* im im))) re)
23.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
12.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4947	1144
1	4947	1144

prune131.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	3	2	5
Picked	1	0	1
Done	1	0	1
Total	81	8	89

Merged error: 12.3b

Counts

89 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))
0.6b	(- (sqrt (+ (* re re) (* im im))) re)
3.8b	(sqrt (* 2.0 (* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))))
26.8b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`-un-lft-identity` `associate-r*`
19×	`times-frac`
16×	`add-cube-cbrt`
13×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-prod` `difference-of-squares`
6×	`add-log-exp`
4×	`sqrt-pow1` `pow-prod-down` `distribute-lft-out--`
3×	`sqrt-div` `associate-r/` `associate-l*`
2×	`flip3--` `pow1/2` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `div-exp` `*-commutative` `flip-+` `div-inv`

Counts

4 → 85

Calls

4 calls:

15.0ms	(* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms	(- (sqrt (+ (* re re) (* im im))) re)
12.0ms	(sqrt (* 2.0 (* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))))
4.0ms	(sqrt (+ (* re re) (* im im)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
24.0ms	(sqrt (* 2.0 (* im (/ im (- (sqrt (+ (* re re) (* im im))) re)))))
9.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4919	1281
1	4919	1281

prune106.0ms

Filtered

69 candidates to 97 candidates (-40.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	97	8	105

Merged error: 11.7b

Counts

105 → 8

regimes243.0ms

Accuracy

33.9% (18.3b remaining)

Error of 31.0b against oracle of 12.8b and baseline of 40.4b

bsearch59.0ms

Steps

Iters	Range		Point
0	1.0380434919050938e-26	1.0615436355507401e-26	1.049793563727917e-26
6	6.879610921486782e-101	4.747545620305833e-100	1.4225952660417887e-100
6	1.5504740844715768e-181	1.3715114345915616e-180	9.700144651592025e-181
6	-1.2965913153833709e-149	-2.2510289479756733e-150	-2.4849948128403756e-150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	78
1	53	78

end0.0ms

sample936.0ms

Algorithm

intervals

Results

300.0ms	6030×	body	80	valid
193.0ms	677×	body	2560	valid
119.0ms	521×	body	1280	valid
100.0ms	290×	body	5120	valid
48.0ms	266×	body	640	valid
22.0ms	147×	body	320	valid
6.0ms	69×	body	160	valid

Details

analyze330.0ms

sample29.0ms

simplify3.0ms

prune6.0ms

localize11.0ms

rewrite27.0ms

series44.0ms

simplify32.0ms

prune122.0ms

localize14.0ms

rewrite47.0ms

series27.0ms

simplify74.0ms

prune138.0ms

localize12.0ms

rewrite36.0ms

series51.0ms

simplify60.0ms

prune131.0ms

localize13.0ms

rewrite42.0ms

series52.0ms

simplify60.0ms

prune106.0ms

regimes243.0ms

bsearch59.0ms

simplify2.0ms

end0.0ms

sample936.0ms

Profiling