Details

analyze463.0ms (5.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample40.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	30×	body	2048	valid
9.0ms	176×	body	128	valid
6.0ms	28×	body	1024	valid
2.0ms	6×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	14×	body	128	invalid
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify219.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 32.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_435`
13×	`*-un-lft-identity_binary64_414`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
7×	`add-cube-cbrt_binary64_446`
6×	`times-frac_binary64_420` `difference-of-squares_binary64_383` `sqrt-prod_binary64_429` `associate-/l*_binary64_361`
5×	`pow1_binary64_472`
4×	`flip3--_binary64_418` `flip--_binary64_389`
3×	`distribute-lft-out--_binary64_368`
2×	`sqrt-div_binary64_430` `diff-log_binary64_503` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `prod-exp_binary64_460` `frac-2neg_binary64_425` `pow1/2_binary64_491` `cbrt-unprod_binary64_444` `div-sub_binary64_419` `associate-/r*_binary64_360` `rem-sqrt-square_binary64_427`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series530.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
128.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4930	1975
1	4930	1975

prune125.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 6.4b

Counts

83 → 9

Compiler

Compiled 2097 to 1147 computations (45.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite113.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_420`
438×	`add-sqr-sqrt_binary64_435`
363×	`*-un-lft-identity_binary64_414`
289×	`add-cube-cbrt_binary64_446`
74×	`difference-of-squares_binary64_383`
71×	`associate-/r*_binary64_360`
40×	`sqrt-prod_binary64_429`
37×	`distribute-lft-out--_binary64_368`
25×	`add-exp-log_binary64_449`
17×	`div-inv_binary64_411`
15×	`div-exp_binary64_462`
13×	`add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
6×	`pow1_binary64_472` `cbrt-undiv_binary64_445`
5×	`associate-/r/_binary64_362`
3×	`1-exp_binary64_455` `flip3--_binary64_418` `rec-exp_binary64_461` `flip--_binary64_389` `associate-/l*_binary64_361`
2×	`sqrt-div_binary64_430` `diff-log_binary64_503` `sub-neg_binary64_407`
1×	`clear-num_binary64_413` `inv-pow_binary64_496` `pow-flip_binary64_485` `sqrt-pow1_binary64_431` `frac-2neg_binary64_425` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 352

Calls

4 calls:

26.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series560.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
118.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify183.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4983	16279
1	4983	16279

prune756.0ms (9.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	362	2	364
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	363	10	373

Merged error: 6.3b

Counts

373 → 10

Compiler

Compiled 12712 to 7073 computations (44.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_435`
17×	`*-un-lft-identity_binary64_414`
13×	`add-cube-cbrt_binary64_446` `associate-r_binary64_356`
10×	`times-frac_binary64_420`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
7×	`pow1_binary64_472`
6×	`associate-l_binary64_357`
5×	`flip3--_binary64_418` `sqrt-prod_binary64_429` `flip--_binary64_389`
4×	`difference-of-squares_binary64_383`
2×	`distribute-lft-out--_binary64_368` `sqrt-div_binary64_430` `associate-*l/_binary64_359` `diff-log_binary64_503` `prod-exp_binary64_460` `sub-neg_binary64_407` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `frac-times_binary64_424`
1×	`div-inv_binary64_411` `-commutative_binary64_347` `sqrt-pow1_binary64_431` `cbrt-undiv_binary64_445` `pow-prod-down_binary64_482` `pow1/2_binary64_491` `associate-r/_binary64_358` `div-exp_binary64_462` `rem-sqrt-square_binary64_427`

Counts

4 → 79

Calls

4 calls:

16.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series537.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
129.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4995	2223
1	4995	2223

prune106.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	92	9	101

Merged error: 6.3b

Counts

101 → 9

Compiler

Compiled 2257 to 1232 computations (45.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
3.9b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_414`
12×	`add-sqr-sqrt_binary64_435`
9×	`add-cube-cbrt_binary64_446` `sqrt-prod_binary64_429` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`times-frac_binary64_420` `add-log-exp_binary64_450`
6×	`associate-/l*_binary64_361`
5×	`pow1_binary64_472`
4×	`flip3--_binary64_418` `sqrt-div_binary64_430` `flip--_binary64_389`
3×	`div-inv_binary64_411`
2×	`distribute-lft-out--_binary64_368` `diff-log_binary64_503` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`distribute-rgt-out--_binary64_370` `clear-num_binary64_413` `difference-of-squares_binary64_383` `sqrt-pow1_binary64_431` `frac-sub_binary64_423` `prod-exp_binary64_460` `frac-2neg_binary64_425` `pow1/2_binary64_491` `cbrt-unprod_binary64_444` `sub-div_binary64_421` `associate-/r*_binary64_360` `rem-sqrt-square_binary64_427`

Counts

4 → 72

Calls

4 calls:

15.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
10.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series610.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2))
172.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5058	2131

prune96.0ms (1.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	83	10	93

Merged error: 6.3b

Counts

93 → 10

Compiler

Compiled 2292 to 1290 computations (43.7% saved)

regimes1.0s (12.6%)

Compiler: Compiled 5112 to 3820 computations (25.3% saved)

bsearch65.0ms (0.8%)

Steps

Iters	Range		Point
9	5.0348965124159976e-43	6.30620444132888e-36	1.4325920982277539e-42
8	-1.0322269454701605e+98	-2.7621719849249905e+94	-1.0164007120358223e+98

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	58
1	101	58

end0.0ms (0%)

sample2.3s (28.3%)

Algorithm

1×

intervals

Results

316.0ms	1206×	body	2048	valid
280.0ms	5148×	body	128	valid
148.0ms	708×	body	1024	valid
138.0ms	412×	body	4096	valid
60.0ms	358×	body	512	valid
35.0ms	679×	body	128	nan
22.0ms	399×	body	128	invalid
17.0ms	168×	body	256	valid

Compiler

Compiled 1354 to 1003 computations (25.9% saved)

Details

analyze463.0ms (5.7%)

sample40.0ms (0.5%)

simplify219.0ms (2.7%)

prune4.0ms (0%)

localize13.0ms (0.2%)

rewrite36.0ms (0.4%)

series530.0ms (6.6%)

simplify71.0ms (0.9%)

prune125.0ms (1.5%)

localize12.0ms (0.2%)

rewrite113.0ms (1.4%)

series560.0ms (6.9%)

simplify183.0ms (2.3%)

prune756.0ms (9.4%)

localize11.0ms (0.1%)

rewrite42.0ms (0.5%)

series537.0ms (6.6%)

simplify58.0ms (0.7%)

prune106.0ms (1.3%)

localize12.0ms (0.1%)

rewrite41.0ms (0.5%)

series610.0ms (7.6%)

simplify60.0ms (0.7%)

prune96.0ms (1.2%)

regimes1.0s (12.6%)

bsearch65.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (28.3%)

Profiling