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 (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

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)

localize11.0ms (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))

rewrite58.0ms (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:

19.0ms	(.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))))

series364.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
110.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
56.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
37.0ms	(.f64 3 (.f64 v v))

simplify83.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5421	3693

prune254.0ms (6.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	137	5	142

Merged error: 0b

Counts

142 → 5

Compiler

Compiled 4360 to 3272 computations (25% saved)

localize17.0ms (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))

rewrite58.0ms (1.5%)

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)))))
7.0ms	(.f64 3 (.f64 v v))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))

series527.0ms (13.2%)

Counts

4 → 12

Calls

4 calls:

322.0ms	(.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)))
116.0ms	(.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))))
37.0ms	(.f64 3 (.f64 v v))

simplify104.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4947	3773
1	4947	3773

prune246.0ms (6.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	140	5	145

Merged error: 0b

Counts

145 → 5

Compiler

Compiled 4246 to 3196 computations (24.7% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`associate-l_binary64_1740`
20×	`add-sqr-sqrt_binary64_1821` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
18×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799` `times-frac_binary64_1805`
16×	`frac-times_binary64_1809`
14×	`pow1_binary64_1860` `sqrt-div_binary64_1816`
13×	`flip--_binary64_1774` `flip3--_binary64_1803`
12×	`associate-*r/_binary64_1741` `sqrt-prod_binary64_1815`
9×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
8×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748`
6×	`pow-prod-down_binary64_1870`
5×	`associate-*l/_binary64_1742`
4×	`sub-neg_binary64_1792` `cancel-sign-sub-inv_binary64_1765`
3×	`add-log-exp_binary64_1838`
2×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833` `-commutative_binary64_1730` `associate-r*_binary64_1739`
1×	`unswap-sqr_binary64_1767` `pow1/2_binary64_1879` `sqrt-pow1_binary64_1817` `div-inv_binary64_1796` `rem-sqrt-square_binary64_1812`

Counts

3 → 100

Calls

3 calls:

20.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))) (-.f64 1 (*.f64 v v))))
7.0ms	(.f64 3 (.f64 v v))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))

series255.0ms (6.4%)

Counts

3 → 9

Calls

3 calls:

163.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v)))) (-.f64 1 (*.f64 v v))))
54.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
38.0ms	(.f64 3 (.f64 v v))

simplify56.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5401	2980

prune163.0ms (4.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	109	5	114

Merged error: 0b

Counts

114 → 5

Compiler

Compiled 3037 to 2253 computations (25.8% saved)

localize16.0ms (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))

rewrite36.0ms (0.9%)

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)))))
6.0ms	(.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)))))))

series456.0ms (11.5%)

Counts

4 → 12

Calls

4 calls:

251.0ms	(log.f64 (exp.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))))
108.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
62.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
35.0ms	(.f64 3 (.f64 v v))

simplify59.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4911	2328
1	4911	2328

prune176.0ms (4.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	112	5	117

Merged error: 0b

Counts

117 → 5

Compiler

Compiled 3131 to 2374 computations (24.2% saved)

regimes49.0ms (1.2%)

Compiler: Compiled 420 to 338 computations (19.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	29
1	54	29

end0.0ms (0%)

sample661.0ms (16.6%)

Algorithm

1×

intervals

Results

411.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 135 to 110 computations (18.5% saved)

Details

analyze5.0ms (0.1%)

sample18.0ms (0.5%)

simplify246.0ms (6.2%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

rewrite58.0ms (1.5%)

series364.0ms (9.2%)

simplify83.0ms (2.1%)

prune254.0ms (6.4%)

localize17.0ms (0.4%)

rewrite58.0ms (1.5%)

series527.0ms (13.2%)

simplify104.0ms (2.6%)

prune246.0ms (6.2%)

localize11.0ms (0.3%)

rewrite42.0ms (1%)

series255.0ms (6.4%)

simplify56.0ms (1.4%)

prune163.0ms (4.1%)

localize16.0ms (0.4%)

rewrite36.0ms (0.9%)

series456.0ms (11.5%)

simplify59.0ms (1.5%)

prune176.0ms (4.4%)

regimes49.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample661.0ms (16.6%)

Profiling