Details

analyze329.0ms (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)

sample35.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	201×	body	80	valid
5.0ms	19×	body	2560	valid
4.0ms	17×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	10×	body	5120	valid
1.0ms	3×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify306.0ms (7.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	250	23
1	250	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: 37.0b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite208.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_575`
7×	`add-log-exp_binary64_555`
6×	`*-un-lft-identity_binary64_590`
4×	`add-cube-cbrt_binary64_561` `sqrt-prod_binary64_569` `pow1_binary64_532`
3×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
2×	`flip-+_binary64_615` `difference-of-squares_binary64_619` `sqrt-div_binary64_570` `flip3-+_binary64_588`
1×	`rem-sqrt-square_binary64_578` `sub-neg_binary64_594` `+-commutative_binary64_657` `flip--_binary64_616` `flip3--_binary64_589` `pow1/2_binary64_522` `distribute-lft-out--_binary64_635` `sqrt-pow1_binary64_571` `diff-log_binary64_501` `sum-log_binary64_500`

Counts

3 → 40

Calls

3 calls:

191.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(+.f64 (.f64 re re) (.f64 im im))

series157.0ms (4%)

Counts

3 → 9

Calls

3 calls:

62.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
56.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
39.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify127.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4757	769
1	4757	769

prune64.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Merged error: 7.7b

Counts

50 → 6

Compiler

Compiled 1059 to 478 computations (54.9% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_532`
2×	`sqrt-pow1_binary64_571` `sqrt-div_binary64_570` `associate-*r/_binary64_651`
1×	`pow-prod-down_binary64_513` `add-cbrt-cube_binary64_562` `flip--_binary64_616` `add-cube-cbrt_binary64_561` `add-exp-log_binary64_554` `add-log-exp_binary64_555` `*-un-lft-identity_binary64_590` `sqrt-prod_binary64_569` `flip3--_binary64_589` `pow1/2_binary64_522` `add-sqr-sqrt_binary64_575`

Counts

1 → 13

Calls

1 calls:

6.0ms

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

series108.0ms (2.8%)

Counts

1 → 3

Calls

1 calls:

108.0ms

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

simplify141.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4960	255
1	4960	255

prune21.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	16	6	22

Merged error: 7.7b

Counts

22 → 6

Compiler

Compiled 323 to 223 computations (31% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

9.6b	(-.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)
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite47.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_575`
9×	`sqrt-prod_binary64_569`
7×	`add-cube-cbrt_binary64_561` `*-un-lft-identity_binary64_590` `pow1_binary64_532`
6×	`add-log-exp_binary64_555` `sqrt-div_binary64_570`
4×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
3×	`rem-sqrt-square_binary64_578` `flip-+_binary64_615` `pow1/2_binary64_522` `sqrt-pow1_binary64_571` `flip3-+_binary64_588`
1×	`sub-neg_binary64_594` `flip--_binary64_616` `flip3--_binary64_589` `diff-log_binary64_501`

Counts

4 → 56

Calls

4 calls:

30.0ms	(-.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)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series208.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(-.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)))
46.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
45.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify116.0ms (3%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5047	931

prune88.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	68	6	74

Merged error: 7.7b

Counts

74 → 6

Compiler

Compiled 2556 to 732 computations (71.4% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

13.0b	(-.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 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite49.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_575`
9×	`sqrt-prod_binary64_569`
7×	`add-cube-cbrt_binary64_561` `*-un-lft-identity_binary64_590` `pow1_binary64_532`
6×	`add-log-exp_binary64_555` `sqrt-div_binary64_570`
4×	`add-cbrt-cube_binary64_562` `add-exp-log_binary64_554`
3×	`rem-sqrt-square_binary64_578` `flip-+_binary64_615` `pow1/2_binary64_522` `sqrt-pow1_binary64_571` `flip3-+_binary64_588`
1×	`sub-neg_binary64_594` `flip--_binary64_616` `flip3--_binary64_589` `diff-log_binary64_501`

Counts

4 → 56

Calls

4 calls:

32.0ms	(-.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 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series206.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(-.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 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))) re)
51.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
43.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify119.0ms (3%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4834	931
1	4834	931

prune87.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	68	6	74

Merged error: 7.7b

Counts

74 → 6

Compiler

Compiled 2582 to 713 computations (72.4% saved)

regimes171.0ms (4.3%)

Compiler: Compiled 392 to 292 computations (25.5% saved)

bsearch47.0ms (1.2%)

Steps

Iters	Range	Point
7	7.751200769140125e-47	5.4722822310152775e-45	7.856956966104623e-47
0	-3.9437321239986167e-91	-3.823494762580694e-91	-3.8836134432896556e-91
7	-2.109590175105431e+132	-4.587634791172327e+130	-7.894340736738551e+130

Iters

Range

Point

7.751200769140125e-47

5.4722822310152775e-45

7.856956966104623e-47

-3.9437321239986167e-91

-3.823494762580694e-91

-3.8836134432896556e-91

-2.109590175105431e+132

-4.587634791172327e+130

-7.894340736738551e+130

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	67	132
1	67	132

end0.0ms (0%)

sample1.2s (31.3%)

Algorithm

1×

intervals

Results

296.0ms	6103×	body	80	valid
181.0ms	660×	body	2560	valid
115.0ms	8000×	pre	80	true
111.0ms	478×	body	1280	valid
90.0ms	273×	body	5120	valid
49.0ms	271×	body	640	valid
20.0ms	139×	body	320	valid
7.0ms	76×	body	160	valid

Compiler

Compiled 199 to 133 computations (33.2% saved)

Details

analyze329.0ms (8.4%)

sample35.0ms (0.9%)

simplify306.0ms (7.8%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

rewrite208.0ms (5.3%)

series157.0ms (4%)

simplify127.0ms (3.2%)

prune64.0ms (1.6%)

localize8.0ms (0.2%)

rewrite6.0ms (0.2%)

series108.0ms (2.8%)

simplify141.0ms (3.6%)

prune21.0ms (0.5%)

localize15.0ms (0.4%)

rewrite47.0ms (1.2%)

series208.0ms (5.3%)

simplify116.0ms (3%)

prune88.0ms (2.2%)

localize20.0ms (0.5%)

rewrite49.0ms (1.3%)

series206.0ms (5.2%)

simplify119.0ms (3%)

prune87.0ms (2.2%)

regimes171.0ms (4.3%)

bsearch47.0ms (1.2%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample1.2s (31.3%)

Profiling