Details

analyze271.0ms (3.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample45.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	133×	body	256	valid
11.0ms	280×	pre	128	true
6.0ms	48×	body	512	valid
4.0ms	75×	body	128	valid
1.0ms	24×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify398.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (303.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	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

Error

54.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
27.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1805`
14×	`*-un-lft-identity_binary64_1783`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
8×	`add-cube-cbrt_binary64_1818` `add-log-exp_binary64_1822`
6×	`difference-of-squares_binary64_1752` `associate-/l*_binary64_1728` `sqrt-prod_binary64_1799` `times-frac_binary64_1789`
5×	`pow1_binary64_1844`
4×	`flip3--_binary64_1787` `cancel-sign-sub-inv_binary64_1749` `flip--_binary64_1758`
3×	`distribute-lft-out--_binary64_1735`
2×	`associate-/l/_binary64_1730` `diff-log_binary64_1875` `sqrt-div_binary64_1800` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `sub-neg_binary64_1776`
1×	`div-sub_binary64_1788` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `pow1/2_binary64_1863` `associate-/r*_binary64_1727` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series273.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
62.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify93.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune101.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Error

0.1b

Counts

87 → 4

Compiler

Compiled 2063 to 1224 computations (40.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
22×	`times-frac_binary64_1789`
20×	`*-un-lft-identity_binary64_1783`
17×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
13×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
11×	`associate-/l*_binary64_1728`
10×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
8×	`add-log-exp_binary64_1822`
6×	`associate-/r/_binary64_1729`
5×	`distribute-lft-out_binary64_1734` `associate-/r*_binary64_1727`
4×	`flip-+_binary64_1757` `div-inv_binary64_1780` `flip3-+_binary64_1786` `pow1_binary64_1844`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `+-commutative_binary64_1713` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `sum-log_binary64_1874` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series453.0ms (6%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
154.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
63.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune149.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Error

0.0b

Counts

115 → 5

Compiler

Compiled 3137 to 1928 computations (38.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
0.3b	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))

rewrite73.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

242×	`times-frac_binary64_1789`
114×	`*-un-lft-identity_binary64_1783`
106×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
61×	`add-exp-log_binary64_1821`
47×	`add-cbrt-cube_binary64_1819`
37×	`div-exp_binary64_1834`
26×	`div-inv_binary64_1780`
25×	`cbrt-undiv_binary64_1817`
19×	`associate-/l*_binary64_1728`
18×	`associate-/r/_binary64_1729`
15×	`associate-*r/_binary64_1725`
13×	`associate-/r*_binary64_1727`
8×	`prod-exp_binary64_1832`
6×	`cbrt-unprod_binary64_1816` `add-log-exp_binary64_1822`
4×	`distribute-lft-out_binary64_1734` `1-exp_binary64_1827` `pow1_binary64_1844`
3×	`frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `flip-+_binary64_1757` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `flip3-+_binary64_1786` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 226

Calls

4 calls:

18.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
15.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series564.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
177.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
165.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
32.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify153.0ms (2%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4894	8594
1	4894	8594

prune349.0ms (4.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	236	2	238
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	238	5	243

Error

Counts

243 → 5

Compiler

Compiled 7042 to 4061 computations (42.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 1 (/.f64 -1/2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))))
0.3b	(/.f64 -1/2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

rewrite107.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

651×	`times-frac_binary64_1789`
400×	`*-un-lft-identity_binary64_1783`
296×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
81×	`associate-/r*_binary64_1727`
52×	`distribute-lft-out_binary64_1734`
40×	`associate-/r/_binary64_1729`
32×	`add-exp-log_binary64_1821`
23×	`div-inv_binary64_1780`
20×	`add-cbrt-cube_binary64_1819`
19×	`div-exp_binary64_1834`
17×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
10×	`cbrt-undiv_binary64_1817`
9×	`associate-/l*_binary64_1728`
6×	`add-log-exp_binary64_1822`
5×	`pow1_binary64_1844`
3×	`1-exp_binary64_1827` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `rec-exp_binary64_1833`
1×	`flip3--_binary64_1787` `inv-pow_binary64_1868` `pow-flip_binary64_1857` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

4 → 399

Calls

4 calls:

20.0ms	(/.f64 1 (/.f64 -1/2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))))
12.0ms	(/.f64 -1/2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series512.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(/.f64 1 (/.f64 -1/2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))))
174.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
113.0ms	(/.f64 -1/2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
34.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify219.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

411 → 411

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5014	17116

prune839.0ms (11.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	410	1	411
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	411	5	416

Error

Counts

416 → 5

Compiler

Compiled 13586 to 8403 computations (38.1% saved)

regimes388.0ms (5.1%)

Accuracy

Total 0.1b remaining (99.5%)

Threshold costs 0.1b (99.5%)

Compiler

Compiled 5116 to 3898 computations (23.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	24
1	60	24

end0.0ms (0%)

sample2.3s (31%)

Algorithm

1×

intervals

Results

362.0ms	3775×	body	256	valid
286.0ms	8875×	pre	128	true
200.0ms	1433×	body	512	valid
138.0ms	2792×	body	128	valid
42.0ms	875×	body	128	nan

Compiler

Compiled 1315 to 1003 computations (23.7% saved)

Details

analyze271.0ms (3.6%)

sample45.0ms (0.6%)

simplify398.0ms (5.3%)

prune4.0ms (0%)

localize14.0ms (0.2%)

rewrite35.0ms (0.5%)

series273.0ms (3.6%)

simplify93.0ms (1.2%)

prune101.0ms (1.3%)

localize17.0ms (0.2%)

rewrite48.0ms (0.6%)

series453.0ms (6%)

simplify69.0ms (0.9%)

prune149.0ms (2%)

localize14.0ms (0.2%)

rewrite73.0ms (1%)

series564.0ms (7.5%)

simplify153.0ms (2%)

prune349.0ms (4.6%)

localize13.0ms (0.2%)

rewrite107.0ms (1.4%)

series512.0ms (6.8%)

simplify219.0ms (2.9%)

prune839.0ms (11.1%)

regimes388.0ms (5.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (31%)

Profiling