Details

analyze660.0ms (19.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample55.0ms (1.6%)

Algorithm

1×

intervals

Results

28.0ms	85×	body	1024	valid
7.0ms	41×	body	512	valid
5.0ms	97×	body	128	valid
3.0ms	10×	body	2048	valid
2.0ms	23×	body	256	valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify218.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5949	8

prune7.0ms (0.2%)

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: 0.0b

Counts

2 → 1

Compiler

Compiled 10 to 10 computations (0% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0b	(+.f64 1 (exp.f64 x))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 28

Calls

2 calls:

6.0ms	(+.f64 1 (exp.f64 x))
4.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

series69.0ms (2.1%)

Counts

2 → 6

Calls

2 calls:

47.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
23.0ms	(+.f64 1 (exp.f64 x))

simplify79.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5000	368

prune24.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	2	35

Merged error: 0b

Counts

35 → 2

Compiler

Compiled 328 to 232 computations (29.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (sqrt.f64 2) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))
0.1b	(.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))
0.5b	(/.f64 x (sqrt.f64 2))

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-l_binary64` `sqrt-prod_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`flip3-+_binary64` `associate-r_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `associate-+r+_binary64` `frac-times_binary64`
1×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 100

Calls

3 calls:

11.0ms	(.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))
5.0ms	(+.f64 (sqrt.f64 2) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))
4.0ms	(/.f64 x (sqrt.f64 2))

series322.0ms (9.6%)

Counts

3 → 9

Calls

3 calls:

183.0ms	(.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))
79.0ms	(/.f64 x (sqrt.f64 2))
60.0ms	(+.f64 (sqrt.f64 2) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))

simplify89.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4944	1886
1	4944	1886

prune125.0ms (3.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	109	2	111

Merged error: 0b

Counts

111 → 2

Compiler

Compiled 2155 to 1770 computations (17.9% saved)

regimes10.0ms (0.3%)

Compiler: Compiled 20 to 19 computations (5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

end0.0ms (0%)

sample1.6s (48.6%)

Algorithm

1×

intervals

Results

865.0ms	2705×	body	1024	valid
235.0ms	1358×	body	512	valid
140.0ms	2985×	body	128	valid
105.0ms	286×	body	2048	valid
72.0ms	666×	body	256	valid

Compiler

Compiled 36 to 35 computations (2.8% saved)

Details

analyze660.0ms (19.7%)

sample55.0ms (1.6%)

simplify218.0ms (6.5%)

prune7.0ms (0.2%)

localize5.0ms (0.2%)

rewrite12.0ms (0.4%)

series69.0ms (2.1%)

simplify79.0ms (2.4%)

prune24.0ms (0.7%)

localize8.0ms (0.2%)

rewrite33.0ms (1%)

series322.0ms (9.6%)

simplify89.0ms (2.7%)

prune125.0ms (3.7%)

regimes10.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.6s (48.6%)

Profiling