Details

analyze334.0ms (7.6%)

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

9.0ms	200×	body	128	valid
6.0ms	17×	body	1024	valid
4.0ms	17×	body	2048	valid
4.0ms	256×	pre	128	true
2.0ms	9×	body	4096	valid
1.0ms	9×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify108.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

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

Error

39.2b

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))
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.0b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms (0.8%)

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:

9.0ms	(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)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

series181.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
28.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4930	1140
1	4930	1140

prune82.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	7	69

Error

8.9b

Counts

69 → 7

Compiler

Compiled 1429 to 635 computations (55.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(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:

4.0ms

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

series62.0ms (1.4%)

Counts

1 → 3

Calls

1 calls:

62.0ms

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

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4956	255
1	4956	255

prune19.0ms (0.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	15	8	23

Error

8.9b

Counts

23 → 8

Compiler

Compiled 321 to 233 computations (27.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (*.f64 2 (-.f64 im re)))
0.1b	(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
0.1b	(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
0.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))

rewrite52.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`sqrt-pow1_binary64_437`
72×	`pow1_binary64_480`
37×	`sqrt-prod_binary64_435`
34×	`sqrt-div_binary64_436`
30×	`add-sqr-sqrt_binary64_441`
25×	`pow-prod-down_binary64_490`
23×	`pow1/2_binary64_499`
20×	`associate-*r/_binary64_361`
14×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `pow-prod-up_binary64_489`
9×	`flip3--_binary64_423` `swap-sqr_binary64_386` `flip--_binary64_394`
8×	`pow-sqr_binary64_392`
7×	`associate-r_binary64_359` `associate-l_binary64_360`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `frac-times_binary64_429` `rem-sqrt-square_binary64_432`
2×	`associate-*l/_binary64_362`
1×	`sqrt-unprod_binary64_439` `rem-square-sqrt_binary64_431` `sqr-abs_binary64_434` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-plus_binary64_482` `*-commutative_binary64_350` `pow2_binary64_500`

Counts

4 → 131

Calls

4 calls:

23.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
6.0ms	(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
6.0ms	(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
5.0ms	(sqrt.f64 (*.f64 2 (-.f64 im re)))

series479.0ms (11%)

Counts

4 → 12

Calls

4 calls:

188.0ms	(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
178.0ms	(sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
59.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))) (sqrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
54.0ms	(sqrt.f64 (*.f64 2 (-.f64 im re)))

simplify75.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4947	1982
1	4947	1982

prune147.0ms (3.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	143	8	151

Error

8.9b

Counts

151 → 8

Compiler

Compiled 2752 to 1817 computations (34% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
5.8b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
13.4b	(-.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_441`
11×	`*-un-lft-identity_binary64_419`
9×	`add-cube-cbrt_binary64_454`
8×	`add-log-exp_binary64_458` `log-prod_binary64_505` `exp-sum_binary64_465`
7×	`sqrt-prod_binary64_435` `pow1_binary64_480`
6×	`exp-prod_binary64_471`
4×	`sqrt-div_binary64_436` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`flip3-+_binary64_422` `difference-of-squares_binary64_388` `log-pow_binary64_508` `flip-+_binary64_393` `cancel-sign-sub-inv_binary64_385`
2×	`exp-diff_binary64_467` `pow1/2_binary64_499` `sqrt-pow1_binary64_437` `log-div_binary64_506`
1×	`sub-neg_binary64_412` `sum-log_binary64_510` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `diff-log_binary64_511` `flip--_binary64_394` `rem-exp-log_binary64_459` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349`

Counts

4 → 66

Calls

4 calls:

11.0ms	(-.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
6.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series172.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
61.0ms	(-.f64 (exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) re)
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5711	1175

prune67.0ms (1.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	78	8	86

Error

8.8b

Counts

86 → 8

Compiler

Compiled 1632 to 685 computations (58% saved)

regimes633.0ms (14.5%)

Accuracy

Total 10.6b remaining (53.3%)

Threshold costs 0b (0%)

Compiler

Compiled 3766 to 2710 computations (28% saved)

bsearch177.0ms (4.1%)

Steps

Iters	Range		Point
9	4.535504168366955e+77	1.2544708847591805e+85	4.5912650619447364e+77
9	2.7768096265269497e+26	1.704305723177486e+32	1.673793550171553e+32
9	2.1053652246543782e-07	0.10143577178192138	0.00014806582749271268
8	-4.934194836533714e-79	-5.938020280856138e-83	-6.0218344330433126e-83
8	-2.270191906557437e-52	-2.2006989416487045e-56	-2.2268645772545896e-52
10	-24.927338592386135	-5.559423211800783e-18	-5.664380019779569e-18
7	-5.478961805018635e+154	-1.6652164707776879e+153	-1.6874163197264964e+153

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	157
1	83	157

end0.0ms (0%)

sample1.4s (32.6%)

Algorithm

1×

intervals

Results

278.0ms	6132×	body	128	valid
144.0ms	505×	body	4096	valid
143.0ms	632×	body	2048	valid
114.0ms	8000×	pre	128	true
68.0ms	392×	body	1024	valid
29.0ms	225×	body	512	valid
12.0ms	114×	body	256	valid

Compiler

Compiled 544 to 382 computations (29.8% saved)

Details

analyze334.0ms (7.6%)

sample34.0ms (0.8%)

simplify108.0ms (2.5%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite33.0ms (0.8%)

series181.0ms (4.1%)

simplify84.0ms (1.9%)

prune82.0ms (1.9%)

localize6.0ms (0.1%)

rewrite5.0ms (0.1%)

series62.0ms (1.4%)

simplify59.0ms (1.3%)

prune19.0ms (0.4%)

localize8.0ms (0.2%)

rewrite52.0ms (1.2%)

series479.0ms (11%)

simplify75.0ms (1.7%)

prune147.0ms (3.4%)

localize14.0ms (0.3%)

rewrite32.0ms (0.7%)

series172.0ms (3.9%)

simplify68.0ms (1.6%)

prune67.0ms (1.5%)

regimes633.0ms (14.5%)

bsearch177.0ms (4.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (32.6%)

Profiling