Details

analyze338.0ms (8.7%)

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)

sample37.0ms (0.9%)

Algorithm

1×

intervals

Results

9.0ms	192×	body	128	valid
6.0ms	24×	body	2048	valid
5.0ms	13×	body	1024	valid
4.0ms	15×	body	4096	valid
4.0ms	256×	pre	128	true
1.0ms	10×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

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: 41.1b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.3%)

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)))
0.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`sqrt-pow1_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 53

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)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

series349.0ms (9%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
58.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
45.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
37.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify39.0ms (1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5173	1116

prune82.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	58	7	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	7	66

Merged error: 11.5b

Counts

66 → 7

Compiler

Compiled 1395 to 633 computations (54.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `flip--_binary64` `sqrt-prod_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

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

series106.0ms (2.7%)

Counts

1 → 3

Calls

1 calls:

106.0ms

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

simplify47.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4965	253
1	4965	253

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: 11.5b

Counts

23 → 9

Compiler

Compiled 359 to 258 computations (28.1% 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)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
8×	`associate-r_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64`
2×	`add-log-exp_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
1×	`cbrt-unprod_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

2 → 51

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series180.0ms (4.6%)

Counts

2 → 6

Calls

2 calls:

117.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
64.0ms	(sqrt.f64 (-.f64 im re))

simplify65.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4964	838
1	4964	838

prune56.0ms (1.4%)

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: 11.5b

Counts

66 → 9

Compiler

Compiled 994 to 610 computations (38.6% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
0.4b	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
0.4b	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
0.4b	(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 im re))) (cbrt.f64 (sqrt.f64 (-.f64 im re))))

rewrite47.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`cbrt-prod_binary64`
58×	`add-sqr-sqrt_binary64`
47×	`sqrt-prod_binary64`
42×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`cbrt-div_binary64` `sqrt-div_binary64`
15×	`swap-sqr_binary64`
11×	`pow1_binary64` `associate-r_binary64` `associate-l_binary64`
9×	`flip3--_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
7×	`difference-of-squares_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 126

Calls

4 calls:

16.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 im re))) (cbrt.f64 (sqrt.f64 (-.f64 im re))))
5.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
5.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
4.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))

series813.0ms (20.8%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 im re))) (cbrt.f64 (sqrt.f64 (-.f64 im re))))
203.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
201.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))
200.0ms	(cbrt.f64 (sqrt.f64 (-.f64 im re)))

simplify79.0ms (2%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4852	2492
1	4852	2492

prune148.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	138	9	147

Merged error: 11.5b

Counts

147 → 9

Compiler

Compiled 3843 to 1289 computations (66.5% saved)

regimes121.0ms (3.1%)

Compiler: Compiled 476 to 387 computations (18.7% saved)

bsearch62.0ms (1.6%)

Steps

Iters	Range		Point
9	1.9017314369682915e+67	2.2981212730082483e+74	1.9328056475004172e+67
10	-1.2486889824601987e+81	-6.683311344954025e+66	-2.539286171271089e+70

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	67
1	50	67

end0.0ms (0%)

sample1.2s (30.7%)

Algorithm

1×

intervals

Results

288.0ms	6035×	body	128	valid
161.0ms	545×	body	4096	valid
148.0ms	639×	body	2048	valid
112.0ms	8000×	pre	128	true
76.0ms	402×	body	1024	valid
36.0ms	254×	body	512	valid
11.0ms	125×	body	256	valid

Compiler

Compiled 193 to 153 computations (20.7% saved)

Details

analyze338.0ms (8.7%)

sample37.0ms (0.9%)

simplify14.0ms (0.4%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

rewrite31.0ms (0.8%)

series349.0ms (9%)

simplify39.0ms (1%)

prune82.0ms (2.1%)

localize6.0ms (0.1%)

rewrite6.0ms (0.2%)

series106.0ms (2.7%)

simplify47.0ms (1.2%)

prune21.0ms (0.5%)

localize7.0ms (0.2%)

rewrite20.0ms (0.5%)

series180.0ms (4.6%)

simplify65.0ms (1.7%)

prune56.0ms (1.4%)

localize14.0ms (0.4%)

rewrite47.0ms (1.2%)

series813.0ms (20.8%)

simplify79.0ms (2%)

prune148.0ms (3.8%)

regimes121.0ms (3.1%)

bsearch62.0ms (1.6%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (30.7%)

Profiling