Details

analyze233.0ms (3.8%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 24 to 21 computations (12.5% saved)

sample78.0ms (1.3%)

Algorithm

1×

intervals

Results

24.0ms	25×	body	4096	valid
19.0ms	180×	body	128	valid
18.0ms	30×	body	2048	valid
4.0ms	9×	body	1024	valid
2.0ms	8×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 47 to 44 computations (6.4% saved)

simplify164.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4970	33
1	4970	33

prune5.0ms (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

30.6b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
0.0b	(pow.f64 (-.f64 A C) 2)
0.7b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
36.5b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
18×	`add-cube-cbrt_binary64_1818`
9×	`cancel-sign-sub-inv_binary64_1749` `times-frac_binary64_1789` `add-log-exp_binary64_1822`
7×	`add-exp-log_binary64_1821` `sqrt-prod_binary64_1799`
6×	`add-cbrt-cube_binary64_1819` `sqrt-div_binary64_1800` `pow1_binary64_1844`
5×	`unpow-prod-down_binary64_1862`
4×	`distribute-lft-out--_binary64_1735` `frac-sub_binary64_1792` `associate--l+_binary64_1720`
3×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `associate-/l_binary64_1728` `pow-unpow_binary64_1860` `flip-+_binary64_1757` `associate-/r_binary64_1727` `diff-log_binary64_1875` `flip3-+_binary64_1786` `flip--_binary64_1758`
2×	`sub-neg_binary64_1776`
1×	`sqr-pow_binary64_1755` `unpow2_binary64_1848` `div-inv_binary64_1780` `pow1/2_binary64_1863` `associate--l-_binary64_1721` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `sqrt-pow1_binary64_1801` `pow-pow_binary64_1855` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 93

Calls

4 calls:

16.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
11.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
5.0ms	(pow.f64 (-.f64 A C) 2)
5.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)

series239.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
79.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B)) PI.f64)
66.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
14.0ms	(pow.f64 (-.f64 A C) 2)

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4965	2955
1	4965	2955

prune163.0ms (2.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	12	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	12	106

Error

20.0b

Counts

106 → 12

Compiler

Compiled 3480 to 1803 computations (48.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))
0.0b	(/.f64 (-.f64 (-.f64 C A) B) B)
0.0b	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) PI.f64))
0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) PI.f64)

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64_1783`
44×	`add-sqr-sqrt_binary64_1805`
37×	`times-frac_binary64_1789`
31×	`add-cube-cbrt_binary64_1818`
13×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `associate-r_binary64_1723`
12×	`distribute-lft-out--_binary64_1735`
9×	`associate-/l*_binary64_1728`
6×	`associate-/r*_binary64_1727` `pow1_binary64_1844`
4×	`difference-of-squares_binary64_1752` `add-log-exp_binary64_1822`
3×	`div-inv_binary64_1780` `associate-l_binary64_1724` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
2×	`associate-/l/_binary64_1730` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `unswap-sqr_binary64_1751`
1×	`flip3--_binary64_1787` `div-sub_binary64_1788` `associate-r/_binary64_1725` `-commutative_binary64_1714` `pow-prod-down_binary64_1854` `flip--_binary64_1758`

Counts

4 → 108

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (-.f64 C A) B) B)
9.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) PI.f64))
7.0ms	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))
5.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) PI.f64)

series129.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(*.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) PI.f64))
36.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) PI.f64)
25.0ms	(/.f64 (-.f64 (-.f64 C A) B) B)
15.0ms	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5170	2442

prune106.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Error

20.0b

Counts

132 → 12

Compiler

Compiled 2685 to 877 computations (67.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))
0.0b	(/.f64 (-.f64 (-.f64 C A) B) B)
0.0b	(.f64 (.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) 180) (/.f64 1 PI.f64))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_1783`
29×	`add-sqr-sqrt_binary64_1805`
27×	`add-exp-log_binary64_1821` `times-frac_binary64_1789`
21×	`add-cube-cbrt_binary64_1818`
17×	`add-cbrt-cube_binary64_1819`
13×	`associate-r_binary64_1723`
12×	`prod-exp_binary64_1832` `distribute-lft-out--_binary64_1735`
8×	`pow1_binary64_1844`
6×	`associate-/l*_binary64_1728` `cbrt-unprod_binary64_1816`
5×	`div-exp_binary64_1834`
4×	`difference-of-squares_binary64_1752`
3×	`associate-/r*_binary64_1727` `cbrt-undiv_binary64_1817` `pow-prod-down_binary64_1854` `add-log-exp_binary64_1822`
2×	`associate-/l/_binary64_1730` `1-exp_binary64_1827` `div-inv_binary64_1780` `rec-exp_binary64_1833`
1×	`flip3--_binary64_1787` `div-sub_binary64_1788` `associate-r/_binary64_1725` `un-div-inv_binary64_1781` `associate-l_binary64_1724` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `flip--_binary64_1758`

Counts

3 → 87

Calls

3 calls:

10.0ms	(.f64 (.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) 180) (/.f64 1 PI.f64))
10.0ms	(/.f64 (-.f64 (-.f64 C A) B) B)
7.0ms	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))

series91.0ms (1.5%)

Counts

3 → 9

Calls

3 calls:

52.0ms	(.f64 (.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B)) 180) (/.f64 1 PI.f64))
25.0ms	(/.f64 (-.f64 (-.f64 C A) B) B)
14.0ms	(atan.f64 (/.f64 (-.f64 (-.f64 C A) B) B))

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5122	1766

prune98.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	96	12	108

Error

20.0b

Counts

108 → 12

Compiler

Compiled 2161 to 971 computations (55.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B))))
0.0b	(pow.f64 (-.f64 A C) 2)
0.7b	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
36.5b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))

rewrite56.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64_1789`
59×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
52×	`add-cube-cbrt_binary64_1818`
16×	`add-exp-log_binary64_1821`
13×	`associate-/r*_binary64_1727`
9×	`add-cbrt-cube_binary64_1819` `cancel-sign-sub-inv_binary64_1749` `add-log-exp_binary64_1822`
7×	`sqrt-prod_binary64_1799` `div-exp_binary64_1834` `pow1_binary64_1844`
6×	`sqrt-div_binary64_1800`
5×	`div-inv_binary64_1780` `unpow-prod-down_binary64_1862`
4×	`distribute-lft-out--_binary64_1735` `frac-sub_binary64_1792` `associate--l+_binary64_1720`
3×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `associate-/l*_binary64_1728` `pow-unpow_binary64_1860` `flip-+_binary64_1757` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `flip3-+_binary64_1786` `flip--_binary64_1758`
2×	`1-exp_binary64_1827` `sub-neg_binary64_1776` `rec-exp_binary64_1833`
1×	`associate-/r/_binary64_1729` `inv-pow_binary64_1868` `sqr-pow_binary64_1755` `unpow2_binary64_1848` `pow-flip_binary64_1857` `pow1/2_binary64_1863` `associate--l-_binary64_1721` `frac-2neg_binary64_1794` `sqrt-pow1_binary64_1801` `pow-pow_binary64_1855` `clear-num_binary64_1782` `rem-sqrt-square_binary64_1796` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 142

Calls

4 calls:

16.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
6.0ms	(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B))))
5.0ms	(pow.f64 (-.f64 A C) 2)

series250.0ms (4%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(/.f64 1 (/.f64 PI.f64 (atan.f64 (/.f64 (-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))) B))))
76.0ms	(-.f64 (-.f64 C A) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B))))
67.0ms	(sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (*.f64 B B)))
16.0ms	(pow.f64 (-.f64 A C) 2)

simplify98.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4989	5604
1	4989	5604

prune232.0ms (3.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	154	12	166

Error

20.0b

Counts

166 → 12

Compiler

Compiled 5315 to 2758 computations (48.1% saved)

regimes550.0ms (8.9%)

Accuracy

Total 9.2b remaining (32.3%)

Threshold costs 0b (0%)

Compiler

Compiled 6286 to 4496 computations (28.5% saved)

bsearch250.0ms (4%)

Steps

Iters	Range		Point
7	2.6919320679959254e+150	6.095502281268703e+152	4.617632627264863e+151
9	3.745338881164429e-198	8.056420300479344e-193	2.405665199649213e-196
8	4.6398571787184005e-302	1.6485377435190205e-298	5.241670643923542e-301
10	-1.7642014608293367e-166	-5.512545412013262e-177	-9.829888247783205e-172
8	-4.550467215923454e+34	-1.6749320969193452e+31	-3.2780186347505555e+32

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	108	175
1	108	175

end0.0ms (0%)

sample3.1s (49.4%)

Algorithm

1×

intervals

Results

677.0ms	857×	body	4096	valid
534.0ms	925×	body	2048	valid
519.0ms	5374×	body	128	valid
196.0ms	449×	body	1024	valid
85.0ms	261×	body	512	valid
27.0ms	134×	body	256	valid

Compiler

Compiled 1010 to 712 computations (29.5% saved)

Details

analyze233.0ms (3.8%)

sample78.0ms (1.3%)

simplify164.0ms (2.6%)

prune5.0ms (0.1%)

localize14.0ms (0.2%)

rewrite48.0ms (0.8%)

series239.0ms (3.9%)

simplify73.0ms (1.2%)

prune163.0ms (2.6%)

localize8.0ms (0.1%)

rewrite41.0ms (0.7%)

series129.0ms (2.1%)

simplify73.0ms (1.2%)

prune106.0ms (1.7%)

localize10.0ms (0.2%)

rewrite38.0ms (0.6%)

series91.0ms (1.5%)

simplify68.0ms (1.1%)

prune98.0ms (1.6%)

localize15.0ms (0.2%)

rewrite56.0ms (0.9%)

series250.0ms (4%)

simplify98.0ms (1.6%)

prune232.0ms (3.8%)

regimes550.0ms (8.9%)

bsearch250.0ms (4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.1s (49.4%)

Profiling