Details

analyze380.0ms (15.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7544	20
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample19.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify304.0ms (12.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (294.0ms)

Iter	Nodes	Cost
0	7544	20

prune3.0ms (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

0.0b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

rewrite35.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_760`
37×	`times-frac_binary64_766`
30×	`add-sqr-sqrt_binary64_782`
23×	`sqrt-prod_binary64_776` `add-cube-cbrt_binary64_795`
8×	`distribute-lft-out_binary64_711` `difference-of-squares_binary64_729` `associate-/l*_binary64_705`
7×	`div-inv_binary64_757`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`associate-/r*_binary64_704` `distribute-rgt-out_binary64_713`
2×	`associate-/l/_binary64_707` `sqrt-div_binary64_777` `pow1_binary64_821`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `flip3-+_binary64_763` `distribute-rgt1-in_binary64_716` `frac-add_binary64_768` `flip-+_binary64_734` `+-commutative_binary64_690` `sum-log_binary64_851` `div-exp_binary64_811` `clear-num_binary64_759` `flip--_binary64_735` `flip3--_binary64_764`

Counts

2 → 73

Calls

2 calls:

23.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

series67.0ms (2.8%)

Counts

2 → 6

Calls

2 calls:

38.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
29.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

simplify70.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5135	1630

prune83.0ms (3.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	1	80

Error

Counts

80 → 1

Compiler

Compiled 1623 to 1029 computations (36.6% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite117.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_766`
129×	`*-un-lft-identity_binary64_760`
123×	`add-sqr-sqrt_binary64_782`
122×	`sqrt-prod_binary64_776`
88×	`add-cube-cbrt_binary64_795`
26×	`associate-r_binary64_700`
23×	`add-exp-log_binary64_798`
22×	`associate-l_binary64_701`
18×	`distribute-lft-out_binary64_711` `associate-/r*_binary64_704`
15×	`add-cbrt-cube_binary64_796`
14×	`difference-of-squares_binary64_729` `associate-/l*_binary64_705`
11×	`div-inv_binary64_757`
10×	`pow1_binary64_821`
7×	`div-exp_binary64_811`
6×	`pow-flip_binary64_834`
5×	`unswap-sqr_binary64_728`
4×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `add-log-exp_binary64_799` `distribute-rgt-out_binary64_713`
3×	`frac-2neg_binary64_771` `frac-times_binary64_770` `associate-*r/_binary64_702` `rec-exp_binary64_810` `clear-num_binary64_759` `1-exp_binary64_804`
2×	`flip3-+_binary64_763` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `frac-add_binary64_768` `inv-pow_binary64_845` `sqrt-div_binary64_777` `flip-+_binary64_734` `cbrt-unprod_binary64_793` `pow1/2_binary64_840`
1×	`associate-l/_binary64_703` `distribute-rgt1-in_binary64_716` `distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `sqrt-undiv_binary64_781` `pow-prod-down_binary64_831` `-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 244

Calls

4 calls:

75.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (sqrt.f64 x))))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
4.0ms	(/.f64 1 (sqrt.f64 x))
4.0ms	(/.f64 1 (sqrt.f64 x))

series143.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(.f64 (/.f64 1 (sqrt.f64 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (sqrt.f64 x))))
33.0ms	(/.f64 1 (sqrt.f64 x))
25.0ms	(/.f64 1 (sqrt.f64 x))
24.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))

simplify118.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4952	4786
1	4952	4786

prune349.0ms (14.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	256	1	257

Error

Counts

257 → 1

Compiler

Compiled 6588 to 3710 computations (43.7% saved)

regimes46.0ms (1.9%)

Accuracy

Total 0.0b remaining (9.5%)

Threshold costs 0.0b (9.5%)

Compiler

Compiled 298 to 226 computations (24.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	17
1	29	17

end0.0ms (0%)

sample668.0ms (27.5%)

Algorithm

1×

intervals

Results

428.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 107 to 83 computations (22.4% saved)

Details

analyze380.0ms (15.7%)

sample19.0ms (0.8%)

simplify304.0ms (12.6%)

prune3.0ms (0.1%)

localize9.0ms (0.4%)

rewrite35.0ms (1.5%)

series67.0ms (2.8%)

simplify70.0ms (2.9%)

prune83.0ms (3.4%)

localize11.0ms (0.4%)

rewrite117.0ms (4.8%)

series143.0ms (5.9%)

simplify118.0ms (4.9%)

prune349.0ms (14.4%)

regimes46.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample668.0ms (27.5%)

Profiling