Details

analyze485.0ms (7.1%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	175×	body	128	valid
7.0ms	28×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	10×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify229.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

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: 33.0b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1799`
15×	`add-sqr-sqrt_binary64_1821`
14×	`add-cube-cbrt_binary64_1834`
12×	`times-frac_binary64_1805`
8×	`add-log-exp_binary64_1838`
6×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
5×	`pow1_binary64_1860` `distribute-lft-out_binary64_1750`
4×	`associate-/l*_binary64_1744`
3×	`associate-/r*_binary64_1743` `sqrt-prod_binary64_1815`
2×	`sqrt-div_binary64_1816` `flip--_binary64_1774` `flip3--_binary64_1803` `associate-/l/_binary64_1746` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`sum-log_binary64_1890` `sub-neg_binary64_1792` `clear-num_binary64_1798` `div-exp_binary64_1850` `+-commutative_binary64_1729` `frac-2neg_binary64_1810` `pow1/2_binary64_1879` `diff-log_binary64_1891` `cbrt-undiv_binary64_1833` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `cancel-sign-sub-inv_binary64_1765` `rem-sqrt-square_binary64_1812`

Counts

4 → 72

Calls

4 calls:

10.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series453.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

154.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
117.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
59.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5101	2019

prune552.0ms (8.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	10	85

Merged error: 6.7b

Counts

85 → 10

Compiler

Compiled 10606 to 7169 computations (32.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1821`
18×	`*-un-lft-identity_binary64_1799`
13×	`add-cube-cbrt_binary64_1834` `add-exp-log_binary64_1837` `associate-r_binary64_1739`
11×	`times-frac_binary64_1805`
9×	`add-cbrt-cube_binary64_1835`
8×	`add-log-exp_binary64_1838`
7×	`pow1_binary64_1860`
4×	`prod-exp_binary64_1848` `associate-l_binary64_1740`
3×	`unswap-sqr_binary64_1767` `sqrt-prod_binary64_1815` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`sqrt-div_binary64_1816` `div-exp_binary64_1850` `flip--_binary64_1774` `flip3--_binary64_1803` `cbrt-unprod_binary64_1832` `distribute-lft-out_binary64_1750` `frac-times_binary64_1809` `associate-*l/_binary64_1742`
1×	`sum-log_binary64_1890` `sub-neg_binary64_1792` `+-commutative_binary64_1729` `un-div-inv_binary64_1797` `rec-exp_binary64_1849` `pow1/2_binary64_1879` `associate-r/_binary64_1741` `1-exp_binary64_1843` `diff-log_binary64_1891` `cbrt-undiv_binary64_1833` `sqrt-pow1_binary64_1817` `-commutative_binary64_1730` `div-inv_binary64_1796` `pow-prod-down_binary64_1870` `cancel-sign-sub-inv_binary64_1765` `rem-sqrt-square_binary64_1812`

Counts

4 → 80

Calls

4 calls:

18.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series447.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
130.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4920	2059
1	4920	2059

prune127.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	92	10	102

Merged error: 6.7b

Counts

102 → 10

Compiler

Compiled 2680 to 1578 computations (41.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.2b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.3b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite61.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_1805`
59×	`add-sqr-sqrt_binary64_1821`
44×	`*-un-lft-identity_binary64_1799`
30×	`add-cube-cbrt_binary64_1834`
27×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
14×	`difference-of-squares_binary64_1768`
13×	`associate-/l*_binary64_1744` `sqrt-prod_binary64_1815`
10×	`div-exp_binary64_1850` `associate-/r/_binary64_1745` `cbrt-undiv_binary64_1833`
9×	`associate-/r*_binary64_1743`
7×	`flip--_binary64_1774` `flip3--_binary64_1803` `distribute-lft-out--_binary64_1751`
6×	`add-log-exp_binary64_1838` `prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `div-inv_binary64_1796` `cancel-sign-sub-inv_binary64_1765`
5×	`pow1_binary64_1860`
2×	`sqrt-div_binary64_1816` `clear-num_binary64_1798` `frac-2neg_binary64_1810`
1×	`sub-neg_binary64_1792` `pow1/2_binary64_1879` `diff-log_binary64_1891` `associate-/l/_binary64_1746` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812`

Counts

4 → 136

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
13.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
10.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series996.0ms (14.6%)

Counts

4 → 12

Calls

4 calls:

416.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
335.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
132.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5217	5032

prune317.0ms (4.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	148	10	158

Merged error: 6.6b

Counts

158 → 10

Compiler

Compiled 6967 to 4145 computations (40.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
23.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_1821`
28×	`*-un-lft-identity_binary64_1799`
18×	`add-cube-cbrt_binary64_1834` `times-frac_binary64_1805`
11×	`sqrt-prod_binary64_1815`
10×	`difference-of-squares_binary64_1768`
8×	`add-log-exp_binary64_1838`
7×	`cancel-sign-sub-inv_binary64_1765`
6×	`associate-/r*_binary64_1743` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
5×	`pow1_binary64_1860` `distribute-lft-out--_binary64_1751`
4×	`flip--_binary64_1774` `flip3--_binary64_1803`
3×	`associate-/l*_binary64_1744`
2×	`sqrt-div_binary64_1816` `sub-neg_binary64_1792` `diff-log_binary64_1891` `associate-/r/_binary64_1745`
1×	`clear-num_binary64_1798` `div-exp_binary64_1850` `frac-2neg_binary64_1810` `pow1/2_binary64_1879` `cbrt-undiv_binary64_1833` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812`

Counts

4 → 88

Calls

4 calls:

10.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series650.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

362.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
117.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
110.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4898	2580
1	4898	2580

prune165.0ms (2.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	99	11	110

Merged error: 6.6b

Counts

110 → 11

Compiler

Compiled 3606 to 2250 computations (37.6% saved)

regimes191.0ms (2.8%)

Compiler: Compiled 732 to 573 computations (21.7% saved)

bsearch112.0ms (1.6%)

Steps

Iters	Range	Point
8	1.8214039147413959e+114	3.0936283487967313e+118	2.1578323955249213e+116
11	2.2854952522798188e-282	3.904822145804709e-260	1.4031237401242977e-270
7	-1.2753667153502532e+154	-8.990067059825001e+151	-1.3091834909018501e+152

Iters

Range

Point

1.8214039147413959e+114

3.0936283487967313e+118

2.1578323955249213e+116

2.2854952522798188e-282

3.904822145804709e-260

1.4031237401242977e-270

-1.2753667153502532e+154

-8.990067059825001e+151

-1.3091834909018501e+152

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	100	92
1	100	92

end0.0ms (0%)

sample1.5s (22.1%)

Algorithm

1×

intervals

Results

310.0ms	1188×	body	2048	valid
289.0ms	5184×	body	128	valid
143.0ms	716×	body	1024	valid
117.0ms	363×	body	4096	valid
55.0ms	367×	body	512	valid
36.0ms	692×	body	128	nan
22.0ms	410×	body	128	invalid
21.0ms	182×	body	256	valid

Compiler

Compiled 364 to 274 computations (24.7% saved)

Details

analyze485.0ms (7.1%)

sample39.0ms (0.6%)

simplify229.0ms (3.4%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite33.0ms (0.5%)

series453.0ms (6.6%)

simplify74.0ms (1.1%)

prune552.0ms (8.1%)

localize13.0ms (0.2%)

rewrite42.0ms (0.6%)

series447.0ms (6.5%)

simplify92.0ms (1.3%)

prune127.0ms (1.9%)

localize12.0ms (0.2%)

rewrite61.0ms (0.9%)

series996.0ms (14.6%)

simplify89.0ms (1.3%)

prune317.0ms (4.6%)

localize14.0ms (0.2%)

rewrite39.0ms (0.6%)

series650.0ms (9.5%)

simplify76.0ms (1.1%)

prune165.0ms (2.4%)

regimes191.0ms (2.8%)

bsearch112.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (22.1%)

Profiling