Details

analyze330.0ms (11.4%)

Algorithm

1×

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

sample34.0ms (1.2%)

Algorithm

1×

intervals

Results

8.0ms	180×	body	80	valid
7.0ms	26×	body	2560	valid
5.0ms	23×	body	1280	valid
3.0ms	10×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

prune7.0ms (0.3%)

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: 41.3b

Counts

2 → 1

localize11.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.4b	(+ (sqrt (+ (* re re) (* im im))) re)
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

7.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series13.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

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

simplify69.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	6207	327

prune92.0ms (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	26	7	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	7	34

Merged error: 18.0b

Counts

34 → 7

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
9.7b	(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
30.8b	(sqrt (+ (* re re) (* im im)))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms (1.6%)

Algorithm

1×	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:

19.0ms	(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms	(+ (* (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)))

series26.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

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

simplify69.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4944	1470
1	4944	1470

prune237.0ms (8.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	134	9	143

Merged error: 18.0b

Counts

143 → 9

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
7.0b	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
31.9b	(cbrt (+ (* re re) (* im im)))
31.9b	(cbrt (+ (* re re) (* im im)))

rewrite28.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
8×	`sqrt-prod`
6×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

9.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
8.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
4.0ms	(cbrt (+ (* re re) (* im im)))
4.0ms	(cbrt (+ (* re re) (* im im)))

series107.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
29.0ms	(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
23.0ms	(cbrt (+ (* re re) (* im im)))
21.0ms	(cbrt (+ (* re re) (* im im)))

simplify52.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5028	1392

prune157.0ms (5.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	77	9	86

Merged error: 18.0b

Counts

86 → 9

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (+ (* re re) (* im im))) re)
6.0b	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
22.0b	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
30.8b	(sqrt (+ (* re re) (* im im)))

rewrite38.0ms (1.3%)

Algorithm

1×	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:

11.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
11.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
10.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series46.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
11.0ms	(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify53.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4947	1144
1	4947	1144

prune131.0ms (4.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	4	3	7
Picked	1	0	1
Done	1	0	1
Total	82	9	91

Merged error: 13.1b

Counts

91 → 9

regimes318.0ms (11%)

Accuracy

Total 10.6b remaining (42.9%)

Threshold costs 0b (0%)

bsearch78.0ms (2.7%)

Steps

Iters	Range		Point
6	5.226028430322971e+69	5.970315257023613e+70	5.816453865787388e+70
7	4.66264676870647e-196	2.1492410711440557e-194	3.499018610539718e-195
6	-5.9084836314411574e-201	-8.870844897620785e-202	-9.044521588158757e-202
9	-6.130611767705085e+170	-9.119445814816622e+165	-9.234847622570144e+165

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	80
1	71	80

end0.0ms (0%)

sample898.0ms (31%)

Algorithm

1×

intervals

Results

277.0ms	5944×	body	80	valid
194.0ms	730×	body	2560	valid
116.0ms	530×	body	1280	valid
94.0ms	284×	body	5120	valid
48.0ms	284×	body	640	valid
20.0ms	157×	body	320	valid
6.0ms	71×	body	160	valid

Details

analyze330.0ms (11.4%)

sample34.0ms (1.2%)

simplify3.0ms (0.1%)

prune7.0ms (0.3%)

localize11.0ms (0.4%)

rewrite11.0ms (0.4%)

series13.0ms (0.4%)

simplify69.0ms (2.4%)

prune92.0ms (3.2%)

localize13.0ms (0.5%)

rewrite47.0ms (1.6%)

series26.0ms (0.9%)

simplify69.0ms (2.4%)

prune237.0ms (8.2%)

localize14.0ms (0.5%)

rewrite28.0ms (1%)

series107.0ms (3.7%)

simplify52.0ms (1.8%)

prune157.0ms (5.4%)

localize12.0ms (0.4%)

rewrite38.0ms (1.3%)

series46.0ms (1.6%)

simplify53.0ms (1.8%)

prune131.0ms (4.5%)

regimes318.0ms (11%)

bsearch78.0ms (2.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample898.0ms (31%)

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