Details

analyze678.0ms (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)

sample62.0ms (0.8%)

Algorithm

1×

intervals

Results

20.0ms	206×	body	128	valid
9.0ms	20×	body	2048	valid
7.0ms	256×	pre	128	true
4.0ms	7×	body	4096	valid
3.0ms	9×	body	1024	valid
2.0ms	9×	body	512	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify203.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

prune5.0ms (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: 35.7b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize21.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
26.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite49.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

18.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
16.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series291.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

199.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
47.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify137.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4923	947
1	4923	947

prune137.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	46	8	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	8	55

Merged error: 7.2b

Counts

55 → 8

Compiler

Compiled 1205 to 540 computations (55.2% saved)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite10.0ms (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:

9.0ms

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

series109.0ms (1.4%)

Counts

1 → 3

Calls

1 calls:

108.0ms

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

simplify102.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4956	255
1	4956	255

prune38.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	16	8	24

Merged error: 7.2b

Counts

24 → 8

Compiler

Compiled 356 to 247 computations (30.6% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))
0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
26.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite82.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_441`
25×	`sqrt-prod_binary64_435`
17×	`*-un-lft-identity_binary64_419`
11×	`add-cube-cbrt_binary64_454`
10×	`pow1_binary64_480`
9×	`associate-r_binary64_359`
6×	`sqrt-div_binary64_436` `difference-of-squares_binary64_388` `add-log-exp_binary64_458` `associate-l_binary64_360` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
4×	`pow1/2_binary64_499` `unswap-sqr_binary64_387` `sqrt-pow1_binary64_437`
3×	`pow-prod-down_binary64_490` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
2×	`associate-*r/_binary64_361` `rem-sqrt-square_binary64_432`
1×	`flip3-+_binary64_422` `sub-neg_binary64_412` `sqrt-unprod_binary64_439` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350` `flip-+_binary64_393` `diff-log_binary64_511`

Counts

4 → 85

Calls

4 calls:

27.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
19.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
14.0ms	(sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series419.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
134.0ms	(sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))
50.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
42.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify156.0ms (2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4907	2012
1	4907	2012

prune173.0ms (2.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	97	8	105

Merged error: 7.2b

Counts

105 → 8

Compiler

Compiled 2288 to 897 computations (60.8% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

9.7b	(-.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
26.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
26.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
26.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite84.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_441`
9×	`sqrt-prod_binary64_435`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
7×	`pow1_binary64_480`
6×	`sqrt-div_binary64_436` `add-log-exp_binary64_458`
4×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`flip3-+_binary64_422` `pow1/2_binary64_499` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385` `rem-sqrt-square_binary64_432`
1×	`sub-neg_binary64_412` `flip3--_binary64_423` `diff-log_binary64_511` `flip--_binary64_394`

Counts

4 → 59

Calls

4 calls:

46.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series183.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
47.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
39.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
37.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify143.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4923	940
1	4923	940

prune147.0ms (1.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	71	8	79

Merged error: 7.2b

Counts

79 → 8

Compiler

Compiled 2579 to 685 computations (73.4% saved)

regimes1.5s (19.1%)

Compiler: Compiled 4462 to 3099 computations (30.5% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	55	143
1	55	143

end0.0ms (0%)

sample3.0s (38.4%)

Algorithm

1×

intervals

Results

589.0ms	6091×	body	128	valid
330.0ms	565×	body	4096	valid
289.0ms	618×	body	2048	valid
207.0ms	8000×	pre	128	true
149.0ms	386×	body	1024	valid
63.0ms	231×	body	512	valid
20.0ms	109×	body	256	valid

Compiler

Compiled 607 to 402 computations (33.8% saved)

Details

analyze678.0ms (8.7%)

sample62.0ms (0.8%)

simplify203.0ms (2.6%)

prune5.0ms (0.1%)

localize21.0ms (0.3%)

rewrite49.0ms (0.6%)

series291.0ms (3.7%)

simplify137.0ms (1.8%)

prune137.0ms (1.8%)

localize11.0ms (0.1%)

rewrite10.0ms (0.1%)

series109.0ms (1.4%)

simplify102.0ms (1.3%)

prune38.0ms (0.5%)

localize22.0ms (0.3%)

rewrite82.0ms (1.1%)

series419.0ms (5.4%)

simplify156.0ms (2%)

prune173.0ms (2.2%)

localize28.0ms (0.4%)

rewrite84.0ms (1.1%)

series183.0ms (2.3%)

simplify143.0ms (1.8%)

prune147.0ms (1.9%)

regimes1.5s (19.1%)

bsearch5.0ms (0.1%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample3.0s (38.4%)

Profiling