Details

analyze501.0ms (15%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14
0	1	1
1	1	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)

sample54.0ms (1.6%)

Algorithm

1×

intervals

Results

20.0ms	125×	body	2048	nan
11.0ms	256×	body	128	valid
8.0ms	67×	body	1024	nan
3.0ms	35×	body	512	nan
1.0ms	20×	body	256	nan
1.0ms	20×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify149.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14

prune2.0ms (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

Error

28.9b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
26.8b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_3829`
7×	`add-sqr-sqrt_binary64_3851`
6×	`sqrt-prod_binary64_3845`
5×	`add-log-exp_binary64_3868` `add-cube-cbrt_binary64_3864` `pow1_binary64_3890`
4×	`log-prod_binary64_3915` `add-exp-log_binary64_3867`
3×	`add-cbrt-cube_binary64_3865`
2×	`flip3-+_binary64_3832` `flip-+_binary64_3803` `difference-of-squares_binary64_3798` `distribute-lft-out_binary64_3780` `sqrt-div_binary64_3846` `log-div_binary64_3916`
1×	`flip--_binary64_3804` `rem-log-exp_binary64_3870` `difference-of-sqr-1_binary64_3799` `rem-sqrt-square_binary64_3842` `sum-log_binary64_3920` `flip3--_binary64_3833` `pow1/2_binary64_3909` `+-commutative_binary64_3759` `sqrt-pow1_binary64_3847` `log-pow_binary64_3918`

Counts

3 → 45

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
7.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series97.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
30.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
23.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify59.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4931	923
1	4931	923

prune50.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	3	55

Error

Counts

55 → 3

Compiler

Compiled 831 to 552 computations (33.6% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_3851`
15×	`sqrt-prod_binary64_3845`
13×	`*-un-lft-identity_binary64_3829`
12×	`sqrt-div_binary64_3846`
10×	`associate-r_binary64_3769`
8×	`add-cube-cbrt_binary64_3864` `pow1_binary64_3890`
7×	`associate-l_binary64_3770`
6×	`add-exp-log_binary64_3867`
5×	`flip3-+_binary64_3832` `add-log-exp_binary64_3868` `flip-+_binary64_3803` `add-cbrt-cube_binary64_3865`
4×	`unswap-sqr_binary64_3797` `frac-times_binary64_3839`
3×	`pow-prod-down_binary64_3900` `flip--_binary64_3804` `log-prod_binary64_3915` `flip3--_binary64_3833`
2×	`difference-of-squares_binary64_3798` `associate-l/_binary64_3772` `pow1/2_binary64_3909` `log-div_binary64_3916` `associate-r/_binary64_3771` `sqrt-pow1_binary64_3847`
1×	`rem-log-exp_binary64_3870` `difference-of-sqr-1_binary64_3799` `sum-log_binary64_3920` `prod-exp_binary64_3878` `distribute-lft-out--_binary64_3781` `distribute-lft-out_binary64_3780` `+-commutative_binary64_3759` `*-commutative_binary64_3760` `cbrt-unprod_binary64_3862` `log-pow_binary64_3918` `sqrt-unprod_binary64_3849`

Counts

3 → 68

Calls

3 calls:

13.0ms	(*.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))))
2.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))

series111.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

44.0ms	(log.f64 (+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))))
36.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
31.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify72.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4977	1681
1	4977	1681

prune85.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	77	3	80

Error

Counts

80 → 3

Compiler

Compiled 1518 to 1152 computations (24.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))))
0.0b	(+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
5.7b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))
26.8b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite35.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_3829`
13×	`log-prod_binary64_3915`
12×	`sqrt-prod_binary64_3845` `add-sqr-sqrt_binary64_3851`
9×	`add-cube-cbrt_binary64_3864` `exp-sum_binary64_3875`
8×	`pow1_binary64_3890`
6×	`add-log-exp_binary64_3868` `exp-prod_binary64_3881`
5×	`add-exp-log_binary64_3867`
4×	`add-cbrt-cube_binary64_3865` `difference-of-squares_binary64_3798` `sqrt-div_binary64_3846` `log-div_binary64_3916` `log-pow_binary64_3918`
2×	`flip3-+_binary64_3832` `flip--_binary64_3804` `difference-of-sqr-1_binary64_3799` `flip-+_binary64_3803` `flip3--_binary64_3833` `pow1/2_binary64_3909` `distribute-lft-out_binary64_3780` `sqrt-pow1_binary64_3847` `exp-diff_binary64_3877`
1×	`rem-exp-log_binary64_3869` `rem-log-exp_binary64_3870` `rem-sqrt-square_binary64_3842` `sum-log_binary64_3920` `+-commutative_binary64_3759`

Counts

4 → 70

Calls

4 calls:

9.0ms	(+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
9.0ms	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))))
7.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series159.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))
42.0ms	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1))))))
34.0ms	(+.f64 x (exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) 1)))))
23.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify60.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4771	1228
1	4771	1228

prune69.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	82	3	85

Error

Counts

85 → 3

Compiler

Compiled 1233 to 829 computations (32.8% saved)

regimes34.0ms (1%)

Accuracy

Total 0.0b remaining (2.7%)

Threshold costs 0.0b (2.7%)

Compiler

Compiled 156 to 124 computations (20.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample1.7s (51.9%)

Algorithm

1×

intervals

Results

646.0ms	4071×	body	2048	nan
342.0ms	8000×	body	128	valid
254.0ms	2004×	body	1024	nan
89.0ms	944×	body	512	nan
35.0ms	524×	body	256	nan
18.0ms	533×	body	128	nan
2.0ms	9×	body	4096	nan

Compiler

Compiled 62 to 51 computations (17.7% saved)

Details

analyze501.0ms (15%)

sample54.0ms (1.6%)

simplify149.0ms (4.4%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite21.0ms (0.6%)

series97.0ms (2.9%)

simplify59.0ms (1.8%)

prune50.0ms (1.5%)

localize9.0ms (0.3%)

rewrite24.0ms (0.7%)

series111.0ms (3.3%)

simplify72.0ms (2.1%)

prune85.0ms (2.5%)

localize10.0ms (0.3%)

rewrite35.0ms (1.1%)

series159.0ms (4.7%)

simplify60.0ms (1.8%)

prune69.0ms (2.1%)

regimes34.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.7s (51.9%)

Profiling