Details

analyze211.0ms (6.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample23.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify182.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	165	17
1	165	17

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: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize17.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
6×	`associate-/l*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `associate-/r/_binary64`
3×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

3 → 100

Calls

3 calls:

12.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series105.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
37.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
22.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify71.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5072	2078

prune144.0ms (4.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	108	2	110

Merged error: 0b

Counts

110 → 2

Compiler

Compiled 2245 to 1828 computations (18.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite146.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

714×	`times-frac_binary64`
690×	`*-un-lft-identity_binary64`
480×	`add-sqr-sqrt_binary64`
424×	`sqrt-prod_binary64`
286×	`add-cube-cbrt_binary64`
128×	`difference-of-squares_binary64`
106×	`distribute-lft-out_binary64`
64×	`distribute-lft-out--_binary64`
54×	`associate-/l*_binary64`
24×	`sqrt-div_binary64`
20×	`associate-/r/_binary64`
14×	`associate-/r*_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-/l/_binary64` `div-sub_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3--_binary64` `flip--_binary64`

Counts

4 → 513

Calls

4 calls:

33.0ms	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x)))
11.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (+.f64 1 x))
4.0ms	(sqrt.f64 (+.f64 1 x))

series117.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
28.0ms	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x)))
25.0ms	(sqrt.f64 (+.f64 1 x))
22.0ms	(sqrt.f64 (+.f64 1 x))

simplify186.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

525 → 525

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4942	15872
1	4942	15872

prune1.3s (40.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	525	0	525
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	525	2	527

Merged error: 0b

Counts

527 → 2

Compiler

Compiled 14112 to 11498 computations (18.5% saved)

regimes43.0ms (1.3%)

Compiler: Compiled 212 to 189 computations (10.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	17
1	22	17

end0.0ms (0%)

sample632.0ms (19.4%)

Algorithm

1×

intervals

Results

433.0ms

8000×

body

128

valid

Compiler

Compiled 51 to 47 computations (7.8% saved)

Details

analyze211.0ms (6.5%)

sample23.0ms (0.7%)

simplify182.0ms (5.6%)

prune4.0ms (0.1%)

localize17.0ms (0.5%)

rewrite33.0ms (1%)

series105.0ms (3.2%)

simplify71.0ms (2.2%)

prune144.0ms (4.4%)

localize10.0ms (0.3%)

rewrite146.0ms (4.5%)

series117.0ms (3.6%)

simplify186.0ms (5.7%)

prune1.3s (40.9%)

regimes43.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample632.0ms (19.4%)

Profiling