Details

analyze462.0ms (7.4%)

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)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	167×	body	128	valid
8.0ms	32×	body	2048	valid
5.0ms	15×	body	4096	valid
4.0ms	23×	body	1024	valid
3.0ms	18×	body	128	invalid
2.0ms	11×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	8×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify230.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (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: 33.5b

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 (.f64 4 a) c))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1783`
13×	`*-un-lft-identity_binary64_1762`
9×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
8×	`add-log-exp_binary64_1798`
7×	`add-cube-cbrt_binary64_1794`
6×	`times-frac_binary64_1768` `difference-of-squares_binary64_1731` `sqrt-prod_binary64_1777` `associate-/l*_binary64_1709`
5×	`pow1_binary64_1820`
4×	`flip3--_binary64_1766` `flip--_binary64_1737`
3×	`distribute-lft-out--_binary64_1716`
2×	`diff-log_binary64_1851` `associate-/l/_binary64_1711` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `sub-neg_binary64_1755` `sqrt-div_binary64_1778`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `div-sub_binary64_1767` `prod-exp_binary64_1808` `clear-num_binary64_1761` `associate-/r*_binary64_1708` `div-inv_binary64_1759` `cbrt-unprod_binary64_1792` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`

Counts

4 → 70

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series516.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify99.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune126.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 5.7b

Counts

83 → 10

Compiler

Compiled 2155 to 1298 computations (39.8% 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 (*.f64 4 a) c))) b) 2)))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite114.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_1768`
438×	`add-sqr-sqrt_binary64_1783`
363×	`*-un-lft-identity_binary64_1762`
289×	`add-cube-cbrt_binary64_1794`
74×	`difference-of-squares_binary64_1731`
71×	`associate-/r*_binary64_1708`
40×	`sqrt-prod_binary64_1777`
37×	`distribute-lft-out--_binary64_1716`
25×	`add-exp-log_binary64_1797`
17×	`div-inv_binary64_1759`
15×	`div-exp_binary64_1810`
13×	`add-cbrt-cube_binary64_1795`
8×	`add-log-exp_binary64_1798`
6×	`cbrt-undiv_binary64_1793` `pow1_binary64_1820`
5×	`associate-/r/_binary64_1710`
3×	`flip3--_binary64_1766` `flip--_binary64_1737` `associate-/l*_binary64_1709` `1-exp_binary64_1803` `rec-exp_binary64_1809`
2×	`diff-log_binary64_1851` `sub-neg_binary64_1755` `sqrt-div_binary64_1778`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `inv-pow_binary64_1844` `clear-num_binary64_1761` `pow-flip_binary64_1833` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`

Counts

4 → 352

Calls

4 calls:

28.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series538.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify178.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5071	16279

prune806.0ms (13%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	360	4	364
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	363	11	374

Merged error: 5.6b

Counts

374 → 11

Compiler

Compiled 12760 to 7717 computations (39.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_1783`
17×	`*-un-lft-identity_binary64_1762`
13×	`add-cube-cbrt_binary64_1794` `associate-r_binary64_1704`
10×	`times-frac_binary64_1768`
9×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
8×	`add-log-exp_binary64_1798`
7×	`pow1_binary64_1820`
6×	`associate-l_binary64_1705`
5×	`flip3--_binary64_1766` `sqrt-prod_binary64_1777` `flip--_binary64_1737`
4×	`difference-of-squares_binary64_1731`
2×	`diff-log_binary64_1851` `frac-times_binary64_1772` `prod-exp_binary64_1808` `unswap-sqr_binary64_1730` `associate-*l/_binary64_1707` `distribute-lft-out--_binary64_1716` `cbrt-unprod_binary64_1792` `sub-neg_binary64_1755` `sqrt-div_binary64_1778`
1×	`rem-sqrt-square_binary64_1775` `pow-prod-down_binary64_1830` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `associate-r/_binary64_1706` `sqrt-pow1_binary64_1779` `-commutative_binary64_1695` `pow1/2_binary64_1839`

Counts

4 → 79

Calls

4 calls:

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

series526.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
124.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4945	2222
1	4945	2222

prune104.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	92	10	102

Merged error: 5.6b

Counts

102 → 10

Compiler

Compiled 2308 to 1381 computations (40.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.0b	(/.f64 1 (sqrt.f64 2))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1783`
22×	`*-un-lft-identity_binary64_1762`
20×	`add-cube-cbrt_binary64_1794`
18×	`times-frac_binary64_1768`
16×	`sqrt-prod_binary64_1777`
8×	`add-log-exp_binary64_1798` `add-exp-log_binary64_1797`
7×	`pow1_binary64_1820`
6×	`associate-/r*_binary64_1708` `add-cbrt-cube_binary64_1795`
3×	`flip3--_binary64_1766` `pow-flip_binary64_1833` `flip--_binary64_1737` `associate-/l*_binary64_1709`
2×	`diff-log_binary64_1851` `difference-of-squares_binary64_1731` `div-exp_binary64_1810` `sqrt-pow1_binary64_1779` `sub-neg_binary64_1755` `sqrt-div_binary64_1778` `pow1/2_binary64_1839`
1×	`rem-sqrt-square_binary64_1775` `frac-2neg_binary64_1773` `inv-pow_binary64_1844` `clear-num_binary64_1761` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `distribute-lft-out--_binary64_1716` `1-exp_binary64_1803` `rec-exp_binary64_1809`

Counts

4 → 85

Calls

4 calls:

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

series306.0ms (4.9%)

Counts

4 → 10

Calls

4 calls:

120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
70.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.0ms	(/.f64 1 (sqrt.f64 2))

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5033	1524

prune127.0ms (2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	95	10	105

Merged error: 5.6b

Counts

105 → 10

Compiler

Compiled 2608 to 1834 computations (29.7% saved)

regimes184.0ms (3%)

Compiler: Compiled 510 to 441 computations (13.5% saved)

bsearch114.0ms (1.8%)

Steps

Iters	Range		Point
9	250566454504151.5	3.764613681933625e+19	7.957206871783919e+17
10	3.0752939460482864e-143	1.2187648676017627e-130	2.6856742787563955e-139
9	-1.1728433930348086e+159	-6.078197847532872e+152	-3.625373603204043e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	108	94
1	108	94

end0.0ms (0%)

sample1.5s (23.4%)

Algorithm

1×

intervals

Results

285.0ms	5217×	body	128	valid
277.0ms	1114×	body	2048	valid
141.0ms	719×	body	1024	valid
124.0ms	406×	body	4096	valid
56.0ms	371×	body	512	valid
34.0ms	695×	body	128	nan
23.0ms	397×	body	128	invalid
19.0ms	173×	body	256	valid

Compiler

Compiled 291 to 228 computations (21.6% saved)

Details

analyze462.0ms (7.4%)

sample42.0ms (0.7%)

simplify230.0ms (3.7%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series516.0ms (8.3%)

simplify99.0ms (1.6%)

prune126.0ms (2%)

localize12.0ms (0.2%)

rewrite114.0ms (1.8%)

series538.0ms (8.7%)

simplify178.0ms (2.9%)

prune806.0ms (13%)

localize11.0ms (0.2%)

rewrite42.0ms (0.7%)

series526.0ms (8.5%)

simplify70.0ms (1.1%)

prune104.0ms (1.7%)

localize14.0ms (0.2%)

rewrite31.0ms (0.5%)

series306.0ms (4.9%)

simplify48.0ms (0.8%)

prune127.0ms (2%)

regimes184.0ms (3%)

bsearch114.0ms (1.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (23.4%)

Profiling