Details

analyze266.0ms (9.8%)

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)

sample54.0ms (2%)

Algorithm

1×

intervals

Results

20.0ms	132×	body	2048	nan
11.0ms	256×	body	128	valid
8.0ms	63×	body	1024	nan
3.0ms	35×	body	512	nan
1.0ms	18×	body	256	nan
0.0ms	15×	body	128	nan
0.0ms	1×	body	4096	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify241.0ms (8.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (146.0ms)

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

31.4b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
29.1b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

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

series62.0ms (2.3%)

Counts

2 → 12

Calls

2 calls:

35.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
27.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 177 to 157 computations (11.3% saved)

simplify67.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5081	540

prune38.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	2	43

Error

Counts

43 → 2

Compiler

Compiled 546 to 356 computations (34.8% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

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)))

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_782`
15×	`sqrt-prod_binary64_776`
12×	`sqrt-div_binary64_777`
11×	`*-un-lft-identity_binary64_760`
10×	`associate-r_binary64_700`
7×	`associate-l_binary64_701`
6×	`add-cube-cbrt_binary64_795` `pow1_binary64_821`
4×	`unswap-sqr_binary64_728` `flip3-+_binary64_763` `add-exp-log_binary64_798` `add-log-exp_binary64_799` `flip-+_binary64_734` `add-cbrt-cube_binary64_796` `frac-times_binary64_770`
3×	`pow-prod-down_binary64_831` `flip--_binary64_735` `flip3--_binary64_764`
2×	`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` `distribute-lft-out--_binary64_712` `+-commutative_binary64_690` `sum-log_binary64_851` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`

Counts

2 → 54

Calls

2 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))))

series70.0ms (2.6%)

Counts

2 → 12

Calls

2 calls:

39.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
30.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

Compiler

Compiled 171 to 153 computations (10.5% saved)

simplify62.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4911	1167
1	4911	1167

prune64.0ms (2.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	66	2	68

Error

Counts

68 → 2

Compiler

Compiled 1149 to 864 computations (24.8% saved)

regimes34.0ms (1.2%)

Accuracy

Total 0.0b remaining (2%)

Threshold costs 0.0b (2%)

Compiler

Compiled 135 to 106 computations (21.5% 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 (62.8%)

Algorithm

1×

intervals

Results

625.0ms	4026×	body	2048	nan
342.0ms	8000×	body	128	valid
255.0ms	2056×	body	1024	nan
93.0ms	1006×	body	512	nan
30.0ms	452×	body	256	nan
15.0ms	462×	body	128	nan
1.0ms	5×	body	4096	nan

Compiler

Compiled 55 to 45 computations (18.2% saved)

Details

analyze266.0ms (9.8%)

sample54.0ms (2%)

simplify241.0ms (8.9%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite13.0ms (0.5%)

series62.0ms (2.3%)

simplify67.0ms (2.5%)

prune38.0ms (1.4%)

localize9.0ms (0.3%)

rewrite20.0ms (0.7%)

series70.0ms (2.6%)

simplify62.0ms (2.3%)

prune64.0ms (2.3%)

regimes34.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.7s (62.8%)

Profiling