Details

analyze467.0ms (7.6%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	37×	body	2048	valid
9.0ms	168×	body	128	valid
5.0ms	17×	body	4096	valid
4.0ms	22×	body	1024	valid
1.0ms	9×	body	512	valid
1.0ms	17×	body	128	invalid
1.0ms	21×	body	128	nan
0.0ms	3×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify367.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (273.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune3.0ms (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: 35.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite33.0ms (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 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series262.0ms (4.3%)

Counts

4 → 36

Calls

4 calls:

113.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
72.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
50.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
27.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4958	2717
1	4958	2717

prune159.0ms (2.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	12	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	12	111

Merged error: 11.6b

Counts

111 → 12

Compiler

Compiled 2853 to 1626 computations (43% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) a))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_1805`
25×	`*-un-lft-identity_binary64_1783`
22×	`associate-r_binary64_1723`
19×	`times-frac_binary64_1789`
17×	`add-cube-cbrt_binary64_1818`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
8×	`difference-of-squares_binary64_1752` `add-log-exp_binary64_1822`
7×	`sqrt-prod_binary64_1799` `pow1_binary64_1844`
4×	`cancel-sign-sub-inv_binary64_1749` `distribute-lft-out--_binary64_1735`
3×	`flip3--_binary64_1787` `associate-l_binary64_1724` `flip--_binary64_1758`
2×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `diff-log_binary64_1875` `sqrt-div_binary64_1800` `unswap-sqr_binary64_1751` `sub-neg_binary64_1776`
1×	`associate-r/_binary64_1725` `div-inv_binary64_1780` `pow1/2_binary64_1863` `cbrt-undiv_binary64_1817` `-commutative_binary64_1714` `div-exp_binary64_1834` `sqrt-pow1_binary64_1801` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796`

Counts

4 → 85

Calls

4 calls:

16.0ms	(.f64 1/3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series252.0ms (4.1%)

Counts

4 → 36

Calls

4 calls:

110.0ms	(.f64 1/3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) a))
67.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
48.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
26.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4958	2925
1	4958	2925

prune140.0ms (2.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	121	12	133

Merged error: 11.6b

Counts

133 → 12

Compiler

Compiled 3191 to 1796 computations (43.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1805`
12×	`*-un-lft-identity_binary64_1783`
8×	`add-cube-cbrt_binary64_1818` `sqrt-prod_binary64_1799` `add-log-exp_binary64_1822`
6×	`cancel-sign-sub-inv_binary64_1749` `pow1_binary64_1844`
4×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `difference-of-squares_binary64_1752` `add-exp-log_binary64_1821` `sqrt-div_binary64_1800` `flip--_binary64_1758`
2×	`pow1/2_binary64_1863` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776`

Counts

4 → 64

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series234.0ms (3.8%)

Counts

4 → 36

Calls

4 calls:

70.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
68.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
50.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
47.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5090	2378

prune163.0ms (2.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	100	12	112

Merged error: 11.6b

Counts

112 → 12

Compiler

Compiled 4080 to 2330 computations (42.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
10.6b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_1822`
7×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`cbrt-prod_binary64_1814`
4×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `cbrt-div_binary64_1815` `cancel-sign-sub-inv_binary64_1749` `flip--_binary64_1758` `pow1_binary64_1844`
2×	`diff-log_binary64_1875` `pow1/3_binary64_1865` `sub-neg_binary64_1776`

Counts

4 → 52

Calls

4 calls:

9.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series361.0ms (5.9%)

Counts

4 → 36

Calls

4 calls:

147.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) b)
96.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
91.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
26.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4944	2681
1	4944	2681

prune141.0ms (2.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	88	12	100

Merged error: 11.6b

Counts

100 → 12

Compiler

Compiled 3377 to 2043 computations (39.5% saved)

regimes880.0ms (14.4%)

Compiler: Compiled 5665 to 4343 computations (23.3% saved)

bsearch62.0ms (1%)

Steps

Iters	Range		Point
7	1.8502524205176364e-56	2.4927491811135052e-54	4.889920063260302e-55
11	-9.974242929839736e+157	-4.553420921657211e+136	-3.877652638047906e+139

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	118	77
1	118	77

end0.0ms (0%)

sample2.1s (34.2%)

Algorithm

1×

intervals

Results

305.0ms	1117×	body	2048	valid
284.0ms	5226×	body	128	valid
136.0ms	679×	body	1024	valid
132.0ms	420×	body	4096	valid
52.0ms	355×	body	512	valid
33.0ms	670×	body	128	nan
20.0ms	381×	body	128	invalid
20.0ms	203×	body	256	valid

Compiler

Compiled 1089 to 831 computations (23.7% saved)

Details

analyze467.0ms (7.6%)

sample40.0ms (0.7%)

simplify367.0ms (6%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite33.0ms (0.5%)

series262.0ms (4.3%)

simplify84.0ms (1.4%)

prune159.0ms (2.6%)

localize11.0ms (0.2%)

rewrite41.0ms (0.7%)

series252.0ms (4.1%)

simplify70.0ms (1.1%)

prune140.0ms (2.3%)

localize14.0ms (0.2%)

rewrite31.0ms (0.5%)

series234.0ms (3.8%)

simplify64.0ms (1%)

prune163.0ms (2.7%)

localize14.0ms (0.2%)

rewrite27.0ms (0.4%)

series361.0ms (5.9%)

simplify84.0ms (1.4%)

prune141.0ms (2.3%)

regimes880.0ms (14.4%)

bsearch62.0ms (1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (34.2%)

Profiling