Details

analyze338.0ms (7.9%)

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)

sample34.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms	202×	body	128	valid
5.0ms	17×	body	4096	valid
4.0ms	256×	pre	128	true
3.0ms	14×	body	2048	valid
3.0ms	14×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify112.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

prune3.0ms (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: 37.2b

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))
0.2b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_441`
8×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `pow1_binary64_480`
6×	`add-cube-cbrt_binary64_454`
5×	`sqrt-prod_binary64_435`
4×	`sqrt-div_binary64_436` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385`
2×	`flip3-+_binary64_422` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `flip3--_binary64_423` `associate-*r/_binary64_361` `flip-+_binary64_393` `flip--_binary64_394`
1×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `sum-log_binary64_510` `distribute-lft-out--_binary64_371` `diff-log_binary64_511` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349`

Counts

4 → 56

Calls

4 calls:

10.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.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))

series182.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
29.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
19.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify85.0ms (2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4930	1140
1	4930	1140

prune87.0ms (2%)

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: 9.7b

Counts

69 → 7

Compiler

Compiled 1469 to 650 computations (55.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_480`
2×	`sqrt-div_binary64_436` `associate-*r/_binary64_361` `sqrt-pow1_binary64_437`
1×	`*-un-lft-identity_binary64_419` `pow-prod-down_binary64_490` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `pow1/2_binary64_499` `add-sqr-sqrt_binary64_441` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394` `sqrt-prod_binary64_435`

Counts

1 → 13

Calls

1 calls:

5.0ms

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

series57.0ms (1.3%)

Counts

1 → 3

Calls

1 calls:

56.0ms

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

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4956	255
1	4956	255

prune21.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	14	9	23

Merged error: 9.6b

Counts

23 → 9

Compiler

Compiled 363 to 253 computations (30.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_441`
17×	`sqrt-prod_binary64_435`
11×	`*-un-lft-identity_binary64_419`
8×	`associate-r_binary64_359`
7×	`add-cube-cbrt_binary64_454` `pow1_binary64_480`
6×	`associate-l_binary64_360`
4×	`sqrt-div_binary64_436` `unswap-sqr_binary64_387` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow-prod-down_binary64_490` `pow1/2_binary64_499` `sqrt-pow1_binary64_437`
2×	`difference-of-squares_binary64_388` `add-log-exp_binary64_458` `flip3--_binary64_423` `associate-*r/_binary64_361` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
1×	`sqrt-unprod_binary64_439` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350` `rem-sqrt-square_binary64_432`

Counts

2 → 51

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
3.0ms	(sqrt.f64 (-.f64 im re))

series94.0ms (2.2%)

Counts

2 → 6

Calls

2 calls:

61.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
33.0ms	(sqrt.f64 (-.f64 im re))

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4954	838
1	4954	838

prune56.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	57	9	66

Merged error: 9.6b

Counts

66 → 9

Compiler

Compiled 1000 to 606 computations (39.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.0b	(log.f64 (sqrt.f64 (-.f64 im re)))
0.3b	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
3.8b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_441`
28×	`log-prod_binary64_505` `sqrt-prod_binary64_435`
23×	`*-un-lft-identity_binary64_419`
20×	`exp-sum_binary64_465`
15×	`add-cube-cbrt_binary64_454`
11×	`associate-r_binary64_359` `pow1_binary64_480`
8×	`sqrt-div_binary64_436`
6×	`unswap-sqr_binary64_387` `exp-prod_binary64_471` `log-pow_binary64_508` `associate-l_binary64_360` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `log-div_binary64_506`
4×	`difference-of-squares_binary64_388` `exp-diff_binary64_467` `add-log-exp_binary64_458` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
3×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437`
2×	`associate-*r/_binary64_361`
1×	`pow-prod-down_binary64_490` `rem-log-exp_binary64_460` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350` `rem-exp-log_binary64_459` `rem-sqrt-square_binary64_432`

Counts

4 → 98

Calls

4 calls:

13.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
6.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
5.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series365.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
133.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
39.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
30.0ms	(sqrt.f64 (-.f64 im re))

simplify76.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6248	1612

prune95.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	110	9	119

Merged error: 9.6b

Counts

119 → 9

Compiler

Compiled 1828 to 1016 computations (44.4% saved)

regimes782.0ms (18.2%)

Compiler: Compiled 4610 to 3397 computations (26.3% saved)

bsearch85.0ms (2%)

Steps

Iters	Range		Point
9	6.881401138394418e+94	5.34897694223027e+103	5.245872734345238e+103
7	7.902451192632932e-94	2.4370021910409217e-92	4.363629092192381e-93
6	-3.860899420892141e-155	-3.595894822361361e-156	-3.659489300718365e-156
3	-4.104867476593262e+135	-3.0525680824585686e+135	-3.1183367945919875e+135

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	104
1	67	104

end0.0ms (0%)

sample1.6s (36.6%)

Algorithm

1×

intervals

Results

302.0ms	6103×	body	128	valid
165.0ms	676×	body	2048	valid
149.0ms	506×	body	4096	valid
115.0ms	8000×	pre	128	true
72.0ms	373×	body	1024	valid
30.0ms	219×	body	512	valid
11.0ms	123×	body	256	valid

Compiler

Compiled 611 to 446 computations (27% saved)

Details

analyze338.0ms (7.9%)

sample34.0ms (0.8%)

simplify112.0ms (2.6%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite32.0ms (0.7%)

series182.0ms (4.2%)

simplify85.0ms (2%)

prune87.0ms (2%)

localize6.0ms (0.1%)

rewrite5.0ms (0.1%)

series57.0ms (1.3%)

simplify57.0ms (1.3%)

prune21.0ms (0.5%)

localize7.0ms (0.2%)

rewrite17.0ms (0.4%)

series94.0ms (2.2%)

simplify73.0ms (1.7%)

prune56.0ms (1.3%)

localize10.0ms (0.2%)

rewrite35.0ms (0.8%)

series365.0ms (8.5%)

simplify76.0ms (1.8%)

prune95.0ms (2.2%)

regimes782.0ms (18.2%)

bsearch85.0ms (2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (36.6%)

Profiling