Details

analyze455.0ms (6.9%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	166×	body	128	valid
7.0ms	31×	body	2048	valid
4.0ms	24×	body	1024	valid
4.0ms	14×	body	4096	valid
2.0ms	12×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	9×	body	256	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify375.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (275.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	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

Error

33.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
21.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite36.0ms (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:

13.0ms	(/.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)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series279.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
38.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify90.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4893	1983
1	4893	1983

prune124.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	77	9	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	9	87

Error

4.5b

Counts

87 → 9

Compiler

Compiled 2152 to 1291 computations (40% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.4b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
7.9b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
21.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
22×	`times-frac_binary64_1789`
21×	`*-un-lft-identity_binary64_1783`
17×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
13×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
12×	`add-sqr-sqrt_binary64_1805`
11×	`associate-/l*_binary64_1728` `add-cube-cbrt_binary64_1818`
6×	`associate-/r/_binary64_1729` `add-log-exp_binary64_1822`
5×	`distribute-lft-out_binary64_1734` `associate-/r*_binary64_1727` `pow1_binary64_1844`
4×	`flip-+_binary64_1757` `div-inv_binary64_1780` `flip3-+_binary64_1786`
3×	`sqrt-prod_binary64_1799`
2×	`sqrt-div_binary64_1800` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `+-commutative_binary64_1713` `pow1/2_binary64_1863` `sum-log_binary64_1874` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `flip--_binary64_1758`

Counts

4 → 102

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
14.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series482.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

207.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
149.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
64.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4961	3218
1	4961	3218

prune150.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	114	9	123

Error

4.4b

Counts

123 → 9

Compiler

Compiled 3317 to 2048 computations (38.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 1/3 (.f64 1 (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
2.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
21.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64_1821`
18×	`add-cbrt-cube_binary64_1819`
15×	`prod-exp_binary64_1832`
10×	`pow1_binary64_1844`
8×	`cbrt-unprod_binary64_1816` `*-un-lft-identity_binary64_1783` `add-log-exp_binary64_1822`
7×	`add-sqr-sqrt_binary64_1805`
6×	`add-cube-cbrt_binary64_1818`
4×	`div-exp_binary64_1834`
3×	`1-exp_binary64_1827` `associate-l_binary64_1724` `sqrt-prod_binary64_1799` `pow-prod-down_binary64_1854`
2×	`flip3--_binary64_1787` `associate-*r/_binary64_1725` `sqrt-div_binary64_1800` `cbrt-undiv_binary64_1817` `flip--_binary64_1758`
1×	`+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `cancel-sign-sub-inv_binary64_1749` `pow1/2_binary64_1863` `diff-log_binary64_1875` `-commutative_binary64_1714` `sum-log_binary64_1874` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776` `associate-r*_binary64_1723`

Counts

4 → 65

Calls

4 calls:

14.0ms	(.f64 1/3 (.f64 1 (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series331.0ms (5%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(.f64 1/3 (.f64 1 (/.f64 (.f64 c -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4887	1593
1	4887	1593

prune282.0ms (4.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	77	9	86

Error

4.4b

Counts

86 → 9

Compiler

Compiled 1917 to 1224 computations (36.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
2.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
21.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_1844`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
8×	`*-un-lft-identity_binary64_1783` `add-log-exp_binary64_1822`
7×	`add-sqr-sqrt_binary64_1805`
6×	`add-cube-cbrt_binary64_1818`
3×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-prod_binary64_1799` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
2×	`flip3--_binary64_1787` `sqrt-div_binary64_1800` `flip--_binary64_1758`
1×	`+-commutative_binary64_1713` `distribute-lft-out_binary64_1734` `flip-+_binary64_1757` `cancel-sign-sub-inv_binary64_1749` `pow1/2_binary64_1863` `associate-l_binary64_1724` `diff-log_binary64_1875` `*-commutative_binary64_1714` `sum-log_binary64_1874` `flip3-+_binary64_1786` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `sub-neg_binary64_1776`

Counts

4 → 57

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series173.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
14.0ms	(.f64 (.f64 3 a) c)

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5147	1126

prune66.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	69	9	78

Error

4.4b

Counts

78 → 9

Compiler

Compiled 1382 to 723 computations (47.7% saved)

regimes1.1s (17.4%)

Accuracy

Total 1.6b remaining (21.9%)

Threshold costs 0b (0%)

Compiler

Compiled 6272 to 4879 computations (22.2% saved)

bsearch88.0ms (1.3%)

Steps

Iters	Range		Point
6	2.301806034112786e+53	2.3160715084359524e+54	2.276445623250457e+54
8	1.0776858093506997e-237	2.1647843930304045e-233	1.094867628068678e-237
8	-8.994821103457546e+83	-1.0532606893601273e+81	-6.684656237783103e+83

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	150	88
1	150	88

end0.0ms (0%)

sample2.1s (32%)

Algorithm

1×

intervals

Results

278.0ms	5273×	body	128	valid
275.0ms	1104×	body	2048	valid
143.0ms	730×	body	1024	valid
120.0ms	388×	body	4096	valid
46.0ms	319×	body	512	valid
34.0ms	639×	body	128	nan
19.0ms	359×	body	128	invalid
18.0ms	186×	body	256	valid

Compiler

Compiled 1186 to 914 computations (22.9% saved)

Details

analyze455.0ms (6.9%)

sample38.0ms (0.6%)

simplify375.0ms (5.7%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite36.0ms (0.5%)

series279.0ms (4.2%)

simplify90.0ms (1.4%)

prune124.0ms (1.9%)

localize13.0ms (0.2%)

rewrite50.0ms (0.8%)

series482.0ms (7.3%)

simplify77.0ms (1.2%)

prune150.0ms (2.3%)

localize13.0ms (0.2%)

rewrite35.0ms (0.5%)

series331.0ms (5%)

simplify72.0ms (1.1%)

prune282.0ms (4.3%)

localize10.0ms (0.2%)

rewrite24.0ms (0.4%)

series173.0ms (2.6%)

simplify49.0ms (0.7%)

prune66.0ms (1%)

regimes1.1s (17.4%)

bsearch88.0ms (1.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (32%)

Profiling