Details

analyze72.0ms (1.7%)

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%	74.9%	25.1%	4
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample14.0ms (0.3%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	5×	body	128	nan
0.0ms	2×	body	128	invalid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify223.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	188	12
1	188	12

prune4.0ms (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: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.3b	(*.f64 y (sqrt.f64 x))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1805`
7×	`add-log-exp_binary64_1822`
6×	`add-cube-cbrt_binary64_1818` `-un-lft-identity_binary64_1783` `associate-r*_binary64_1723`
4×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `associate-+l+_binary64_1716` `sqrt-prod_binary64_1799` `pow1_binary64_1844`
3×	`cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724`
2×	`sum-log_binary64_1874` `unswap-sqr_binary64_1751`
1×	`+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `associate-+l-_binary64_1718` `diff-log_binary64_1875` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `sub-neg_binary64_1776`

Counts

2 → 39

Calls

2 calls:

9.0ms	(*.f64 y (sqrt.f64 x))
9.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

series128.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

64.0ms	(*.f64 y (sqrt.f64 x))
63.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

simplify105.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5082	594

prune43.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	38	7	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	8	46

Merged error: 0.0b

Counts

46 → 8

Compiler

Compiled 681 to 341 computations (49.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_1799`
25×	`add-sqr-sqrt_binary64_1805`
18×	`associate-r_binary64_1723`
15×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
11×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
8×	`sqrt-pow1_binary64_1801`
4×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow1/2_binary64_1863` `associate-l_binary64_1724` `pow-prod-down_binary64_1854` `rem-sqrt-square_binary64_1796` `add-log-exp_binary64_1822`
3×	`unswap-sqr_binary64_1751`
2×	`*-commutative_binary64_1714`

Counts

4 → 88

Calls

4 calls:

11.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
7.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
2.0ms	(sqrt.f64 (sqrt.f64 x))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series449.0ms (11%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt.f64 (sqrt.f64 x))
119.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
104.0ms	(sqrt.f64 (sqrt.f64 x))
88.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

simplify83.0ms (2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5316	1029

prune117.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	102	6	108

Merged error: 0b

Counts

108 → 6

Compiler

Compiled 1722 to 652 computations (62.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
0.4b	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))

rewrite78.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`sqrt-prod_binary64_1799`
33×	`associate-r_binary64_1723`
26×	`add-sqr-sqrt_binary64_1805`
22×	`pow1_binary64_1844`
20×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
18×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854`
5×	`associate-l_binary64_1724`
4×	`sqrt-pow1_binary64_1801` `add-log-exp_binary64_1822`
3×	`*-commutative_binary64_1714` `unswap-sqr_binary64_1751`
2×	`pow1/2_binary64_1863` `rem-sqrt-square_binary64_1796`

Counts

4 → 102

Calls

4 calls:

23.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
19.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
13.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
4.0ms	(sqrt.f64 (sqrt.f64 x))

series486.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

157.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
146.0ms	(sqrt.f64 (sqrt.f64 x))
94.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
88.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))

simplify81.0ms (2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4979	1493
1	4979	1493

prune172.0ms (4.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	114	6	120

Merged error: 0b

Counts

120 → 6

Compiler

Compiled 2492 to 850 computations (65.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
0.5b	(cbrt.f64 (sqrt.f64 x))
0.5b	(cbrt.f64 (sqrt.f64 x))
0.5b	(cbrt.f64 (sqrt.f64 x))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`cbrt-prod_binary64_1814`
44×	`add-sqr-sqrt_binary64_1805`
29×	`sqrt-prod_binary64_1799`
22×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
11×	`swap-sqr_binary64_1750` `pow1_binary64_1844`
9×	`associate-l_binary64_1724` `pow1/3_binary64_1865` `unswap-sqr_binary64_1751` `associate-r_binary64_1723`
6×	`add-exp-log_binary64_1821`
4×	`add-cbrt-cube_binary64_1819` `add-log-exp_binary64_1822`
2×	`pow-prod-up_binary64_1853` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
1×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-plus_binary64_1846` `*-commutative_binary64_1714` `pow2_binary64_1864`

Counts

4 → 98

Calls

4 calls:

12.0ms	(*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
2.0ms	(cbrt.f64 (sqrt.f64 x))
2.0ms	(cbrt.f64 (sqrt.f64 x))
2.0ms	(cbrt.f64 (sqrt.f64 x))

series556.0ms (13.5%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(cbrt.f64 (sqrt.f64 x))
144.0ms	(cbrt.f64 (sqrt.f64 x))
137.0ms	(*.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 (sqrt.f64 x)))
110.0ms	(cbrt.f64 (sqrt.f64 x))

simplify150.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4847	1353
1	4847	1353

prune153.0ms (3.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	110	6	116

Merged error: 0b

Counts

116 → 6

Compiler

Compiled 2349 to 806 computations (65.7% saved)

regimes138.0ms (3.4%)

Compiler: Compiled 704 to 517 computations (26.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms (0%)

sample919.0ms (22.4%)

Algorithm

1×

intervals

Results

334.0ms	7998×	body	128	valid
5.0ms	145×	body	128	nan
3.0ms	68×	body	128	invalid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 245 to 182 computations (25.7% saved)

Details

analyze72.0ms (1.7%)

sample14.0ms (0.3%)

simplify223.0ms (5.4%)

prune4.0ms (0.1%)

localize12.0ms (0.3%)

rewrite20.0ms (0.5%)

series128.0ms (3.1%)

simplify105.0ms (2.5%)

prune43.0ms (1%)

localize8.0ms (0.2%)

rewrite34.0ms (0.8%)

series449.0ms (11%)

simplify83.0ms (2%)

prune117.0ms (2.9%)

localize10.0ms (0.2%)

rewrite78.0ms (1.9%)

series486.0ms (11.8%)

simplify81.0ms (2%)

prune172.0ms (4.2%)

localize11.0ms (0.3%)

rewrite33.0ms (0.8%)

series556.0ms (13.5%)

simplify150.0ms (3.6%)

prune153.0ms (3.7%)

regimes138.0ms (3.4%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample919.0ms (22.4%)

Profiling