Details

analyze344.0ms (7.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample56.0ms (1.2%)

Algorithm

1×

intervals

Results

20.0ms	131×	body	2048	nan
13.0ms	256×	body	128	valid
9.0ms	78×	body	1024	nan
3.0ms	29×	body	512	nan
1.0ms	11×	body	256	nan
0.0ms	15×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify287.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	5604	14

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: 30.9b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
28.7b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_760`
7×	`add-sqr-sqrt_binary64_782`
6×	`sqrt-prod_binary64_776`
5×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799` `pow1_binary64_821`
4×	`add-exp-log_binary64_798` `log-prod_binary64_846`
3×	`add-cbrt-cube_binary64_796`
2×	`log-div_binary64_847` `distribute-lft-out_binary64_711` `flip3-+_binary64_763` `difference-of-squares_binary64_729` `sqrt-div_binary64_777` `flip-+_binary64_734`
1×	`rem-sqrt-square_binary64_773` `sqrt-pow1_binary64_778` `difference-of-sqr-1_binary64_730` `log-pow_binary64_849` `+-commutative_binary64_690` `sum-log_binary64_851` `rem-log-exp_binary64_801` `pow1/2_binary64_840` `flip--_binary64_735` `flip3--_binary64_764`

Counts

3 → 45

Calls

3 calls:

11.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
8.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
8.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

series235.0ms (5%)

Counts

3 → 9

Calls

3 calls:

107.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
79.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
49.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify72.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4891	923
1	4891	923

prune55.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Merged error: 0b

Counts

55 → 2

Compiler

Compiled 837 to 557 computations (33.5% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
0.2b	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
0.2b	(/.f64 3/32 (pow.f64 x 4))
0.6b	(/.f64 1/4 (*.f64 x x))

rewrite56.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_760`
32×	`add-sqr-sqrt_binary64_782`
26×	`add-cube-cbrt_binary64_795`
25×	`times-frac_binary64_766`
16×	`distribute-lft-out--_binary64_712`
14×	`add-exp-log_binary64_798`
13×	`pow1_binary64_821`
12×	`unpow-prod-down_binary64_839`
11×	`add-cbrt-cube_binary64_796`
10×	`cancel-sign-sub-inv_binary64_726` `add-log-exp_binary64_799`
9×	`distribute-lft-out_binary64_711` `log-pow_binary64_849`
8×	`associate-/r*_binary64_704`
6×	`associate-/l*_binary64_705` `log-prod_binary64_846`
5×	`diff-log_binary64_852` `div-exp_binary64_811`
4×	`associate--r+_binary64_696` `sqr-pow_binary64_732`
3×	`cbrt-undiv_binary64_794` `difference-of-squares_binary64_729` `associate--l+_binary64_697`
2×	`frac-2neg_binary64_771` `div-inv_binary64_757` `sum-log_binary64_851` `clear-num_binary64_759` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`
1×	`prod-exp_binary64_809` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `associate--r-_binary64_699` `cbrt-unprod_binary64_793` `associate-+r-_binary64_694`

Counts

4 → 121

Calls

4 calls:

26.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
9.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
5.0ms	(/.f64 1/4 (*.f64 x x))
5.0ms	(/.f64 3/32 (pow.f64 x 4))

series442.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

248.0ms	(-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))
104.0ms	(-.f64 (log.f64 2) (+.f64 (/.f64 3/32 (pow.f64 x 4)) (-.f64 (/.f64 1/4 (*.f64 x x)) (log.f64 x))))
57.0ms	(/.f64 3/32 (pow.f64 x 4))
33.0ms	(/.f64 1/4 (*.f64 x x))

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4931	2312
1	4931	2312

prune214.0ms (4.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	133	2	135

Merged error: 0b

Counts

135 → 2

Compiler

Compiled 2948 to 1989 computations (32.5% saved)

localize17.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.2b	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_782`
15×	`sqrt-prod_binary64_776`
13×	`*-un-lft-identity_binary64_760`
12×	`sqrt-div_binary64_777`
10×	`associate-r_binary64_700`
8×	`add-cube-cbrt_binary64_795` `pow1_binary64_821`
7×	`associate-l_binary64_701`
6×	`add-exp-log_binary64_798`
5×	`flip3-+_binary64_763` `add-log-exp_binary64_799` `flip-+_binary64_734` `add-cbrt-cube_binary64_796`
4×	`unswap-sqr_binary64_728` `frac-times_binary64_770`
3×	`pow-prod-down_binary64_831` `flip--_binary64_735` `log-prod_binary64_846` `flip3--_binary64_764`
2×	`log-div_binary64_847` `associate-l/_binary64_703` `sqrt-pow1_binary64_778` `difference-of-squares_binary64_729` `associate-r/_binary64_702` `pow1/2_binary64_840`
1×	`distribute-lft-out_binary64_711` `prod-exp_binary64_809` `difference-of-sqr-1_binary64_730` `sqrt-unprod_binary64_780` `log-pow_binary64_849` `distribute-lft-out--_binary64_712` `+-commutative_binary64_690` `sum-log_binary64_851` `rem-log-exp_binary64_801` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`

Counts

3 → 68

Calls

3 calls:

16.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
3.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))

series285.0ms (6%)

Counts

3 → 9

Calls

3 calls:

149.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
76.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
60.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify118.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4900	1681
1	4900	1681

prune109.0ms (2.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	77	2	79

Merged error: 0b

Counts

79 → 2

Compiler

Compiled 1507 to 1143 computations (24.2% saved)

regimes52.0ms (1.1%)

Compiler: Compiled 150 to 121 computations (19.3% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	164	26
1	164	26

end0.0ms (0%)

sample2.2s (46.9%)

Algorithm

1×

intervals

Results

863.0ms	4133×	body	2048	nan
446.0ms	8000×	body	128	valid
321.0ms	1998×	body	1024	nan
123.0ms	1036×	body	512	nan
42.0ms	528×	body	256	nan
21.0ms	490×	body	128	nan
3.0ms	11×	body	4096	nan

Compiler

Compiled 65 to 54 computations (16.9% saved)

Details

analyze344.0ms (7.3%)

sample56.0ms (1.2%)

simplify287.0ms (6%)

prune4.0ms (0.1%)

localize14.0ms (0.3%)

rewrite30.0ms (0.6%)

series235.0ms (5%)

simplify72.0ms (1.5%)

prune55.0ms (1.2%)

localize14.0ms (0.3%)

rewrite56.0ms (1.2%)

series442.0ms (9.3%)

simplify83.0ms (1.7%)

prune214.0ms (4.5%)

localize17.0ms (0.4%)

rewrite28.0ms (0.6%)

series285.0ms (6%)

simplify118.0ms (2.5%)

prune109.0ms (2.3%)

regimes52.0ms (1.1%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.2s (46.9%)

Profiling