Details

analyze713.0ms (16.3%)

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)

sample65.0ms (1.5%)

Algorithm

1×

intervals

Results

35.0ms	89×	body	1024	valid
10.0ms	52×	body	512	valid
4.0ms	83×	body	128	valid
3.0ms	24×	body	256	valid
3.0ms	8×	body	2048	valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify211.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5949	8

prune7.0ms (0.1%)

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)

localize13.0ms (0.3%)

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)))

series63.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

40.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
23.0ms	(+.f64 1 (exp.f64 x))

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5000	368

prune27.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	2	35

Merged error: 0b

Counts

35 → 2

Compiler

Compiled 346 to 246 computations (28.9% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(pow.f64 (exp.f64 x) 3)
4.3b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

rewrite54.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`*-un-lft-identity_binary64`
76×	`sqrt-prod_binary64`
56×	`times-frac_binary64`
51×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
25×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
8×	`associate-/r*_binary64` `pow-pow_binary64`
7×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64` `associate-/l*_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `exp-prod_binary64`
4×	`difference-of-squares_binary64` `sqrt-div_binary64`
3×	`unpow2_binary64` `sqr-pow_binary64` `cube-prod_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 152

Calls

4 calls:

20.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
7.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
4.0ms	(pow.f64 (exp.f64 x) 3)
4.0ms	(pow.f64 (exp.f64 x) 2)

series383.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

281.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
43.0ms	(pow.f64 (exp.f64 x) 3)
38.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
21.0ms	(pow.f64 (exp.f64 x) 2)

simplify99.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4920	4717
1	4920	4717

prune234.0ms (5.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	164	2	166

Merged error: 0b

Counts

166 → 2

Compiler

Compiled 4388 to 2998 computations (31.7% 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))

rewrite34.0ms (0.8%)

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))))
4.0ms	(/.f64 x (sqrt.f64 2))
3.0ms	(+.f64 1/2 (*.f64 x 3/16))

series384.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))
85.0ms	(/.f64 x (sqrt.f64 2))
62.0ms	(+.f64 (sqrt.f64 2) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))
47.0ms	(+.f64 1/2 (*.f64 x 3/16))

simplify74.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5008	2031

prune144.0ms (3.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	123	2	125

Merged error: 0b

Counts

125 → 2

Compiler

Compiled 2393 to 1973 computations (17.6% saved)

regimes13.0ms (0.3%)

Compiler: Compiled 33 to 28 computations (15.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	29
1	26	29

end0.0ms (0%)

sample1.7s (39.8%)

Algorithm

1×

intervals

Results

904.0ms	2688×	body	1024	valid
247.0ms	1322×	body	512	valid
154.0ms	3028×	body	128	valid
121.0ms	307×	body	2048	valid
79.0ms	655×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 62 to 53 computations (14.5% saved)

Details

analyze713.0ms (16.3%)

sample65.0ms (1.5%)

simplify211.0ms (4.8%)

prune7.0ms (0.1%)

localize13.0ms (0.3%)

rewrite12.0ms (0.3%)

series63.0ms (1.4%)

simplify80.0ms (1.8%)

prune27.0ms (0.6%)

localize16.0ms (0.4%)

rewrite54.0ms (1.2%)

series383.0ms (8.7%)

simplify99.0ms (2.3%)

prune234.0ms (5.3%)

localize8.0ms (0.2%)

rewrite34.0ms (0.8%)

series384.0ms (8.8%)

simplify74.0ms (1.7%)

prune144.0ms (3.3%)

regimes13.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.7s (39.8%)

Profiling