Details

analyze682.0ms (17.4%)

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)

sample58.0ms (1.5%)

Algorithm

1×

intervals

Results

27.0ms	82×	body	1024	valid
9.0ms	46×	body	512	valid
5.0ms	100×	body	128	valid
3.0ms	22×	body	256	valid
2.0ms	6×	body	2048	valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify215.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5949	8

prune6.0ms (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 (0.1%)

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 (0.3%)

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:

5.0ms	(+.f64 1 (exp.f64 x))
4.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

series71.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

48.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
23.0ms	(+.f64 1 (exp.f64 x))

simplify79.0ms (2%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4999	368
1	4999	368

prune26.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	3	35

Merged error: 0b

Counts

35 → 3

Compiler

Compiled 341 to 243 computations (28.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
0.0b	(+.f64 1 (exp.f64 x))
0.0b	(+.f64 1 (exp.f64 x))
0.6b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))

rewrite46.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
36×	`sqrt-pow1_binary64`
29×	`pow1_binary64`
28×	`sqrt-div_binary64`
18×	`pow1/2_binary64` `swap-sqr_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64` `associate-l_binary64`
9×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow-prod-up_binary64` `unswap-sqr_binary64` `flip-+_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`frac-times_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `associate-l/_binary64` `sum-log_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

21.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
4.0ms	(+.f64 1 (exp.f64 x))
3.0ms	(+.f64 1 (exp.f64 x))

series214.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
45.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
10.0ms	(+.f64 1 (exp.f64 x))
10.0ms	(+.f64 1 (exp.f64 x))

simplify65.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4918	1842
1	4918	1842

prune129.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	146	3	149

Merged error: 0b

Counts

149 → 3

Compiler

Compiled 2120 to 1528 computations (27.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (*.f64 x 3/16))
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)))
0.4b	(/.f64 x (sqrt.f64 2))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-l_binary64` `sqrt-prod_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/r*_binary64` `pow1_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-r_binary64` `unswap-sqr_binary64` `associate-/l*_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` `+-commutative_binary64` `associate-+r+_binary64` `frac-times_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 111

Calls

4 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))))
5.0ms	(/.f64 x (sqrt.f64 2))
3.0ms	(+.f64 1/2 (*.f64 x 3/16))

series369.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))
73.0ms	(/.f64 x (sqrt.f64 2))
68.0ms	(+.f64 (sqrt.f64 2) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))
53.0ms	(+.f64 1/2 (*.f64 x 3/16))

simplify87.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4930	2031
1	4930	2031

prune138.0ms (3.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	123	3	126

Merged error: 0b

Counts

126 → 3

Compiler

Compiled 2392 to 1974 computations (17.5% saved)

regimes13.0ms (0.3%)

Compiler: Compiled 33 to 30 computations (9.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	7	8

end0.0ms (0%)

sample1.6s (42.1%)

Algorithm

1×

intervals

Results

854.0ms	2642×	body	1024	valid
243.0ms	1353×	body	512	valid
142.0ms	3046×	body	128	valid
110.0ms	293×	body	2048	valid
74.0ms	666×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 49 to 46 computations (6.1% saved)

Details

analyze682.0ms (17.4%)

sample58.0ms (1.5%)

simplify215.0ms (5.5%)

prune6.0ms (0.2%)

localize5.0ms (0.1%)

rewrite12.0ms (0.3%)

series71.0ms (1.8%)

simplify79.0ms (2%)

prune26.0ms (0.7%)

localize7.0ms (0.2%)

rewrite46.0ms (1.2%)

series214.0ms (5.5%)

simplify65.0ms (1.7%)

prune129.0ms (3.3%)

localize8.0ms (0.2%)

rewrite36.0ms (0.9%)

series369.0ms (9.4%)

simplify87.0ms (2.2%)

prune138.0ms (3.5%)

regimes13.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.6s (42.1%)

Profiling