Details

analyze213.0ms (6.1%)

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

15.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify183.0ms (5.2%)

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 (0.9%)

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:

11.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series96.0ms (2.7%)

Counts

3 → 9

Calls

3 calls:

43.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
33.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
19.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify72.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5072	2078

prune135.0ms (3.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	2	110

Merged error: 0b

Counts

110 → 2

Compiler

Compiled 2021 to 1629 computations (19.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite64.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
81×	`*-un-lft-identity_binary64`
61×	`times-frac_binary64`
50×	`difference-of-squares_binary64`
36×	`associate-l_binary64`
32×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`associate-r_binary64` `cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
5×	`associate-/r*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 151

Calls

4 calls:

21.0ms	(.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))
15.0ms	(sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x)))
9.0ms	(/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x)))
1.0ms	(atan.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))))

series142.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x)))
34.0ms	(.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))
33.0ms	(/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x)))
24.0ms	(atan.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))))

simplify84.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5047	3335

prune212.0ms (6.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	163	2	165

Merged error: 0b

Counts

165 → 2

Compiler

Compiled 3922 to 2801 computations (28.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite145.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Rules

436×	`sqrt-prod_binary64`
381×	`*-un-lft-identity_binary64`
268×	`add-sqr-sqrt_binary64`
227×	`times-frac_binary64`
99×	`add-cube-cbrt_binary64`
68×	`difference-of-squares_binary64`
66×	`swap-sqr_binary64`
64×	`distribute-lft-out_binary64`
46×	`distribute-lft-out--_binary64`
36×	`associate-r_binary64` `associate-l_binary64`
33×	`sqrt-pow1_binary64`
28×	`pow1_binary64`
17×	`pow1/2_binary64`
16×	`unswap-sqr_binary64`
14×	`associate-/r/_binary64`
12×	`rem-sqrt-square_binary64` `associate-/l*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow-prod-up_binary64` `sqrt-div_binary64`
8×	`associate-/r*_binary64`
7×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
5×	`pow-prod-down_binary64` `sqr-abs_binary64` `pow-sqr_binary64`
4×	`associate-/l/_binary64` `add-log-exp_binary64`
2×	`flip3--_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `associate-r/_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 339

Calls

4 calls:

54.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
10.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

series144.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
48.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
24.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
21.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify128.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

351 → 351

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4954	7348
1	4954	7348

prune758.0ms (21.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	351	2	353

Merged error: 0b

Counts

353 → 2

Compiler

Compiled 9188 to 7478 computations (18.6% saved)

regimes136.0ms (3.9%)

Compiler: Compiled 1502 to 1289 computations (14.2% 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%)

sample885.0ms (25.3%)

Algorithm

1×

intervals

Results

438.0ms

8000×

body

128

valid

Compiler

Compiled 309 to 267 computations (13.6% saved)

Details

analyze213.0ms (6.1%)

sample23.0ms (0.7%)

simplify183.0ms (5.2%)

prune4.0ms (0.1%)

localize17.0ms (0.5%)

rewrite33.0ms (0.9%)

series96.0ms (2.7%)

simplify72.0ms (2.1%)

prune135.0ms (3.9%)

localize11.0ms (0.3%)

rewrite64.0ms (1.8%)

series142.0ms (4.1%)

simplify84.0ms (2.4%)

prune212.0ms (6.1%)

localize11.0ms (0.3%)

rewrite145.0ms (4.1%)

series144.0ms (4.1%)

simplify128.0ms (3.7%)

prune758.0ms (21.7%)

regimes136.0ms (3.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample885.0ms (25.3%)

Profiling