Details

analyze336.0ms (8.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample32.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	202×	body	128	valid
4.0ms	16×	body	4096	valid
4.0ms	256×	pre	128	true
3.0ms	15×	body	2048	valid
3.0ms	14×	body	1024	valid
1.0ms	4×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify166.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	156	23
1	156	23

prune2.0ms (0.1%)

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: 37.1b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_445`
8×	`*-un-lft-identity_binary64_423` `pow1_binary64_484` `add-log-exp_binary64_462`
6×	`add-cube-cbrt_binary64_458`
5×	`sqrt-prod_binary64_439`
4×	`sqrt-div_binary64_440` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
3×	`cancel-sign-sub-inv_binary64_389` `sqrt-pow1_binary64_441`
2×	`flip-+_binary64_397` `flip3--_binary64_427` `associate-*r/_binary64_365` `flip3-+_binary64_426` `difference-of-squares_binary64_392` `pow1/2_binary64_503` `flip--_binary64_398`
1×	`pow-prod-down_binary64_494` `sub-neg_binary64_416` `diff-log_binary64_515` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `distribute-lft-out--_binary64_375` `sum-log_binary64_514`

Counts

4 → 56

Calls

4 calls:

10.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series353.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
57.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
39.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify64.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5363	1125

prune276.0ms (6.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 7.6b

Counts

69 → 7

Compiler

Compiled 4947 to 3007 computations (39.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(sqrt.f64 (*.f64 2 (-.f64 im re)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_484`
2×	`sqrt-div_binary64_440` `associate-*r/_binary64_365` `sqrt-pow1_binary64_441`
1×	`*-un-lft-identity_binary64_423` `pow-prod-down_binary64_494` `add-cube-cbrt_binary64_458` `sqrt-prod_binary64_439` `add-sqr-sqrt_binary64_445` `flip3--_binary64_427` `add-exp-log_binary64_461` `pow1/2_binary64_503` `add-cbrt-cube_binary64_459` `add-log-exp_binary64_462` `flip--_binary64_398`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

series117.0ms (2.9%)

Counts

1 → 3

Calls

1 calls:

117.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

simplify53.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5019	253

prune35.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	15	8	23

Merged error: 7.6b

Counts

23 → 8

Compiler

Compiled 573 to 426 computations (25.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_445`
17×	`sqrt-prod_binary64_439`
11×	`*-un-lft-identity_binary64_423`
8×	`associate-r_binary64_363`
7×	`add-cube-cbrt_binary64_458` `pow1_binary64_484`
6×	`associate-l_binary64_364`
4×	`sqrt-div_binary64_440` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `unswap-sqr_binary64_391`
3×	`pow-prod-down_binary64_494` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`
2×	`flip3--_binary64_427` `associate-*r/_binary64_365` `distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392` `add-log-exp_binary64_462` `flip--_binary64_398`
1×	`prod-exp_binary64_472` `rem-sqrt-square_binary64_436` `*-commutative_binary64_354` `sqrt-unprod_binary64_443` `cbrt-unprod_binary64_456`

Counts

2 → 51

Calls

2 calls:

11.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series170.0ms (4.2%)

Counts

2 → 6

Calls

2 calls:

114.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
55.0ms	(sqrt.f64 (-.f64 im re))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4962	838
1	4962	838

prune70.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	56	9	65

Merged error: 7.6b

Counts

65 → 9

Compiler

Compiled 1253 to 817 computations (34.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.4b	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
3.8b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

rewrite50.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_445`
23×	`sqrt-prod_binary64_439`
20×	`exp-sum_binary64_469` `log-prod_binary64_509`
18×	`*-un-lft-identity_binary64_423`
12×	`add-cube-cbrt_binary64_458`
11×	`associate-r_binary64_363`
8×	`pow1_binary64_484`
6×	`sqrt-div_binary64_440` `associate-l_binary64_364` `unswap-sqr_binary64_391` `exp-prod_binary64_475`
5×	`add-cbrt-cube_binary64_459`
4×	`exp-diff_binary64_471` `add-exp-log_binary64_461` `log-div_binary64_510`
3×	`flip3--_binary64_427` `log-pow_binary64_512` `distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392` `add-log-exp_binary64_462` `flip--_binary64_398`
2×	`associate-*r/_binary64_365` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`
1×	`pow-prod-down_binary64_494` `prod-exp_binary64_472` `rem-sqrt-square_binary64_436` `rem-exp-log_binary64_463` `*-commutative_binary64_354` `cbrt-unprod_binary64_456`

Counts

3 → 77

Calls

3 calls:

23.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
8.0ms	(sqrt.f64 (-.f64 im re))
6.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

series568.0ms (14.1%)

Counts

3 → 9

Calls

3 calls:

294.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
217.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
56.0ms	(sqrt.f64 (-.f64 im re))

simplify91.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4940	1235
1	4940	1235

prune94.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	86	9	95

Merged error: 7.6b

Counts

95 → 9

Compiler

Compiled 1686 to 1018 computations (39.6% saved)

regimes189.0ms (4.7%)

Compiler: Compiled 697 to 535 computations (23.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	122
1	53	122

end0.0ms (0%)

sample1.2s (29.6%)

Algorithm

1×

intervals

Results

283.0ms	6056×	body	128	valid
149.0ms	531×	body	4096	valid
144.0ms	616×	body	2048	valid
118.0ms	8000×	pre	128	true
73.0ms	417×	body	1024	valid
35.0ms	257×	body	512	valid
11.0ms	123×	body	256	valid

Compiler

Compiled 230 to 150 computations (34.8% saved)

Details

analyze336.0ms (8.4%)

sample32.0ms (0.8%)

simplify166.0ms (4.1%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite33.0ms (0.8%)

series353.0ms (8.8%)

simplify64.0ms (1.6%)

prune276.0ms (6.9%)

localize6.0ms (0.1%)

rewrite6.0ms (0.1%)

series117.0ms (2.9%)

simplify53.0ms (1.3%)

prune35.0ms (0.9%)

localize7.0ms (0.2%)

rewrite18.0ms (0.5%)

series170.0ms (4.2%)

simplify67.0ms (1.7%)

prune70.0ms (1.7%)

localize10.0ms (0.2%)

rewrite50.0ms (1.3%)

series568.0ms (14.1%)

simplify91.0ms (2.3%)

prune94.0ms (2.3%)

regimes189.0ms (4.7%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (29.6%)

Profiling