Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 20 to 16 computations (20% saved)

sample18.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 39 to 32 computations (17.9% saved)

simplify246.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4910	29
1	4910	29

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 38 to 30 computations (21.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
0.0b	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
0.1b	(.f64 3 (.f64 v v))

rewrite57.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_1821`
26×	`associate-l_binary64_1740`
23×	`add-cbrt-cube_binary64_1835` `*-un-lft-identity_binary64_1799` `add-exp-log_binary64_1837`
22×	`add-cube-cbrt_binary64_1834` `times-frac_binary64_1805`
20×	`sqrt-prod_binary64_1815`
18×	`sqrt-div_binary64_1816` `frac-times_binary64_1809`
17×	`pow1_binary64_1860`
15×	`flip--_binary64_1774` `flip3--_binary64_1803`
12×	`associate-r_binary64_1739`
10×	`prod-exp_binary64_1848` `associate-*r/_binary64_1741` `cbrt-unprod_binary64_1832`
9×	`associate-*l/_binary64_1742`
7×	`unswap-sqr_binary64_1767` `pow-prod-down_binary64_1870`
4×	`add-log-exp_binary64_1838`
3×	`*-commutative_binary64_1730`
2×	`distribute-rgt-in_binary64_1749` `sub-neg_binary64_1792` `div-exp_binary64_1850` `distribute-lft-in_binary64_1748` `difference-of-squares_binary64_1768` `cbrt-undiv_binary64_1833` `cancel-sign-sub-inv_binary64_1765`
1×	`pow1/2_binary64_1879` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812`

Counts

4 → 129

Calls

4 calls:

16.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
14.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
7.0ms	(.f64 3 (.f64 v v))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))

series356.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

159.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
105.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
55.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
36.0ms	(.f64 3 (.f64 v v))

simplify83.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5421	3693

prune253.0ms (6.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	3	142

Merged error: 0b

Counts

142 → 3

Compiler

Compiled 4322 to 3242 computations (25% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (exp.f64 (log.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v)))
0.0b	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
0.1b	(.f64 3 (.f64 v v))

rewrite61.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_1821`
29×	`associate-l_binary64_1740`
24×	`*-un-lft-identity_binary64_1799`
23×	`add-cube-cbrt_binary64_1834`
22×	`times-frac_binary64_1805`
20×	`sqrt-prod_binary64_1815`
18×	`sqrt-div_binary64_1816` `frac-times_binary64_1809`
16×	`add-cbrt-cube_binary64_1835`
15×	`exp-diff_binary64_1847` `flip--_binary64_1774` `flip3--_binary64_1803` `add-exp-log_binary64_1837` `log-div_binary64_1886`
14×	`pow1_binary64_1860`
12×	`associate-r_binary64_1739`
10×	`associate-*r/_binary64_1741`
9×	`associate-*l/_binary64_1742`
8×	`unswap-sqr_binary64_1767`
6×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
5×	`pow-prod-down_binary64_1870`
4×	`add-log-exp_binary64_1838`
3×	`*-commutative_binary64_1730`
2×	`distribute-rgt-in_binary64_1749` `sub-neg_binary64_1792` `distribute-lft-in_binary64_1748` `difference-of-squares_binary64_1768` `cancel-sign-sub-inv_binary64_1765`
1×	`log-prod_binary64_1885` `exp-sum_binary64_1845` `div-exp_binary64_1850` `pow1/2_binary64_1879` `cbrt-undiv_binary64_1833` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812`

Counts

4 → 128

Calls

4 calls:

18.0ms	(.f64 (exp.f64 (log.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v)))
14.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
9.0ms	(.f64 3 (.f64 v v))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))

series523.0ms (13.7%)

Counts

4 → 12

Calls

4 calls:

319.0ms	(.f64 (exp.f64 (log.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))))) (-.f64 1 (*.f64 v v)))
117.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
51.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
35.0ms	(.f64 3 (.f64 v v))

simplify109.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4947	3773
1	4947	3773

prune241.0ms (6.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	140	3	143

Merged error: 0b

Counts

143 → 3

Compiler

Compiled 4227 to 3181 computations (24.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
0.0b	(log.f64 (exp.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))))
0.1b	(.f64 3 (.f64 v v))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_1821`
25×	`associate-l_binary64_1740`
22×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799` `times-frac_binary64_1805`
20×	`sqrt-prod_binary64_1815`
14×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
13×	`pow1_binary64_1860`
7×	`unswap-sqr_binary64_1767` `associate-r_binary64_1739`
6×	`sqrt-div_binary64_1816`
5×	`add-log-exp_binary64_1838` `prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
4×	`pow-prod-down_binary64_1870`
3×	`log-prod_binary64_1885` `flip--_binary64_1774` `flip3--_binary64_1803` `log-pow_binary64_1888`
2×	`associate-r/_binary64_1741` `-commutative_binary64_1730` `frac-times_binary64_1809`
1×	`div-exp_binary64_1850` `exp-to-pow_binary64_1861` `pow1/2_binary64_1879` `cbrt-undiv_binary64_1833` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `exp-prod_binary64_1851` `rem-sqrt-square_binary64_1812` `rem-log-exp_binary64_1840` `associate-*l/_binary64_1742`

Counts

4 → 100

Calls

4 calls:

14.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
7.0ms	(.f64 3 (.f64 v v))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
2.0ms	(log.f64 (exp.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))))

series418.0ms (11%)

Counts

4 → 12

Calls

4 calls:

231.0ms	(log.f64 (exp.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))))
104.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
51.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
33.0ms	(.f64 3 (.f64 v v))

simplify60.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4911	2328
1	4911	2328

prune173.0ms (4.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	112	3	115

Merged error: 0b

Counts

115 → 3

Compiler

Compiled 3147 to 2388 computations (24.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (*.f64 v v) 5/8))
0.0b	(.f64 (sqrt.f64 2) (-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (.f64 v v) 5/8)))
0.1b	(*.f64 (pow.f64 v 4) 3/32)
0.1b	(.f64 (.f64 v v) 5/8)

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1821`
16×	`add-exp-log_binary64_1837`
14×	`associate-l_binary64_1740`
13×	`add-cbrt-cube_binary64_1835`
11×	`pow1_binary64_1860` `add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
9×	`add-log-exp_binary64_1838` `associate-r_binary64_1739`
7×	`prod-exp_binary64_1848`
6×	`unswap-sqr_binary64_1767`
5×	`cbrt-unprod_binary64_1832`
4×	`unpow-prod-down_binary64_1878` `sqrt-prod_binary64_1815` `pow-prod-down_binary64_1870`
3×	`distribute-rgt-in_binary64_1749` `sub-neg_binary64_1792` `distribute-lft-in_binary64_1748` `associate--l+_binary64_1736` `*-commutative_binary64_1730` `cancel-sign-sub-inv_binary64_1765`
2×	`associate-*r/_binary64_1741` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `sqr-pow_binary64_1771`
1×	`sum-log_binary64_1890` `pow-to-exp_binary64_1868` `pow-exp_binary64_1867`

Counts

4 → 88

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 2) (-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (.f64 v v) 5/8)))
7.0ms	(-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (*.f64 v v) 5/8))
7.0ms	(.f64 (.f64 v v) 5/8)
6.0ms	(*.f64 (pow.f64 v 4) 3/32)

series213.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(.f64 (sqrt.f64 2) (-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (.f64 v v) 5/8)))
50.0ms	(-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (*.f64 v v) 5/8))
49.0ms	(*.f64 (pow.f64 v 4) 3/32)
38.0ms	(.f64 (.f64 v v) 5/8)

simplify74.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5180	1788

prune132.0ms (3.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	100	3	103

Merged error: 0b

Counts

103 → 3

Compiler

Compiled 2321 to 1809 computations (22.1% saved)

regimes19.0ms (0.5%)

Compiler: Compiled 124 to 102 computations (17.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	33
1	56	33

end0.0ms (0%)

sample633.0ms (16.6%)

Algorithm

1×

intervals

Results

405.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 99 to 82 computations (17.2% saved)

Details

analyze5.0ms (0.1%)

sample18.0ms (0.5%)

simplify246.0ms (6.5%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

rewrite57.0ms (1.5%)

series356.0ms (9.3%)

simplify83.0ms (2.2%)

prune253.0ms (6.6%)

localize14.0ms (0.4%)

rewrite61.0ms (1.6%)

series523.0ms (13.7%)

simplify109.0ms (2.9%)

prune241.0ms (6.3%)

localize14.0ms (0.4%)

rewrite39.0ms (1%)

series418.0ms (11%)

simplify60.0ms (1.6%)

prune173.0ms (4.5%)

localize10.0ms (0.3%)

rewrite42.0ms (1.1%)

series213.0ms (5.6%)

simplify74.0ms (1.9%)

prune132.0ms (3.5%)

regimes19.0ms (0.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample633.0ms (16.6%)

Profiling