Details

analyze454.0ms (8.4%)

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)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	40×	body	2048	valid
9.0ms	171×	body	128	valid
4.0ms	19×	body	1024	valid
3.0ms	9×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	23×	body	128	nan
1.0ms	17×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify222.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0.1%)

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: 32.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (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))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0.8%)

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:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 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)))

series517.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
125.0ms	(-.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))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4930	1975
1	4930	1975

prune125.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 6.1b

Counts

83 → 7

Compiler

Compiled 2064 to 1122 computations (45.6% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_450` `add-sqr-sqrt_binary64_435`
6×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `sqrt-prod_binary64_429` `*-un-lft-identity_binary64_414`
4×	`flip3--_binary64_418` `sqrt-div_binary64_430` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `flip--_binary64_389`
2×	`diff-log_binary64_503` `sqrt-pow1_binary64_431` `sub-neg_binary64_407` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 52

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series352.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5014	1222

prune102.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	63	8	71

Merged error: 6.1b

Counts

71 → 8

Compiler

Compiled 2547 to 1392 computations (45.3% saved)

localize14.0ms (0.3%)

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))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.3b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.8%)

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)))
9.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series637.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

270.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2))
184.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5058	2131

prune109.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	83	9	92

Merged error: 6.0b

Counts

92 → 9

Compiler

Compiled 2463 to 1408 computations (42.8% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

9.5b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
21.2b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
21.2b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_435`
7×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
6×	`cbrt-prod_binary64_442` `add-log-exp_binary64_450`
5×	`pow1_binary64_472`
4×	`flip3--_binary64_418` `cbrt-div_binary64_443` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `flip--_binary64_389`
3×	`sqrt-prod_binary64_429`
2×	`sqrt-div_binary64_430` `pow1/3_binary64_493`
1×	`diff-log_binary64_503` `sqrt-pow1_binary64_431` `sub-neg_binary64_407` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 52

Calls

4 calls:

10.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series653.0ms (12.1%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
173.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
170.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4927	1687
1	4927	1687

prune131.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	65	8	73

Merged error: 6.0b

Counts

73 → 8

Compiler

Compiled 3307 to 1795 computations (45.7% saved)

regimes140.0ms (2.6%)

Compiler: Compiled 624 to 444 computations (28.8% saved)

bsearch62.0ms (1.2%)

Steps

Iters	Range		Point
9	1.359390363693246e-22	4.825546432485297e-13	1.392247260771699e-22
6	-2.3677179713659354e+154	-2.465565162145652e+153	-2.5949872779844862e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	123	70
1	123	70

end0.0ms (0%)

sample1.4s (26.1%)

Algorithm

1×

intervals

Results

275.0ms	5232×	body	128	valid
267.0ms	1074×	body	2048	valid
140.0ms	739×	body	1024	valid
127.0ms	408×	body	4096	valid
54.0ms	363×	body	512	valid
34.0ms	697×	body	128	nan
22.0ms	391×	body	128	invalid
18.0ms	184×	body	256	valid

Compiler

Compiled 313 to 219 computations (30% saved)

Details

analyze454.0ms (8.4%)

sample38.0ms (0.7%)

simplify222.0ms (4.1%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite42.0ms (0.8%)

series517.0ms (9.5%)

simplify69.0ms (1.3%)

prune125.0ms (2.3%)

localize16.0ms (0.3%)

rewrite25.0ms (0.5%)

series352.0ms (6.5%)

simplify67.0ms (1.2%)

prune102.0ms (1.9%)

localize14.0ms (0.3%)

rewrite41.0ms (0.8%)

series637.0ms (11.8%)

simplify58.0ms (1.1%)

prune109.0ms (2%)

localize21.0ms (0.4%)

rewrite33.0ms (0.6%)

series653.0ms (12.1%)

simplify53.0ms (1%)

prune131.0ms (2.4%)

regimes140.0ms (2.6%)

bsearch62.0ms (1.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (26.1%)

Profiling