Details

analyze229.0ms (6.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample26.0ms (0.8%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	80	valid
0.0ms	6×	body	80	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify74.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5045	29

prune6.0ms (0.2%)

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: 13.9b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.6b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.6b	(-.f64 (.f64 b b) (.f64 a a))
9.7b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite88.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

224×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
132×	`*-un-lft-identity_binary64`
100×	`add-cube-cbrt_binary64`
58×	`associate-l_binary64`
46×	`difference-of-squares_binary64`
19×	`associate-r_binary64` `div-inv_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`distribute-lft-out--_binary64`
13×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
4×	`associate-/r*_binary64` `sub-neg_binary64` `associate-/r/_binary64`
3×	`cbrt-unprod_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-sub_binary64` `frac-times_binary64`
2×	`diff-log_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 230

Calls

4 calls:

47.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
14.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
10.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
5.0ms	(-.f64 (.f64 b b) (.f64 a a))

series32.0ms (1%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
10.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
7.0ms	(-.f64 (.f64 b b) (.f64 a a))
3.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify111.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5121	6697

prune263.0ms (7.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	233	9	242
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	235	9	244

Merged error: 0.0b

Counts

244 → 9

Compiler

Compiled 7252 to 3542 computations (51.2% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
0.2b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64`
79×	`*-un-lft-identity_binary64`
60×	`add-exp-log_binary64`
51×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
39×	`add-cbrt-cube_binary64`
29×	`div-exp_binary64`
19×	`prod-exp_binary64`
17×	`cbrt-undiv_binary64`
14×	`distribute-lft-out_binary64` `associate-/l*_binary64`
10×	`cbrt-unprod_binary64`
7×	`div-inv_binary64`
6×	`1-exp_binary64`
5×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`

Counts

2 → 122

Calls

2 calls:

16.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series19.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

11.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
8.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify84.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5096	2615

prune115.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	127	10	137

Merged error: 0b

Counts

137 → 10

Compiler

Compiled 2631 to 1323 computations (49.7% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
0.3b	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
0.3b	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

rewrite89.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

621×	`times-frac_binary64`
410×	`*-un-lft-identity_binary64`
278×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
202×	`add-exp-log_binary64`
120×	`div-exp_binary64`
71×	`associate-/r*_binary64`
66×	`distribute-lft-out_binary64`
62×	`add-cbrt-cube_binary64`
61×	`prod-exp_binary64`
35×	`1-exp_binary64`
31×	`cbrt-undiv_binary64`
28×	`div-inv_binary64`
15×	`rec-exp_binary64`
13×	`cbrt-unprod_binary64`
8×	`associate-/l*_binary64`
6×	`associate-/r/_binary64`
4×	`pow1_binary64`
3×	`associate-/l/_binary64` `add-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `inv-pow_binary64` `pow-flip_binary64` `flip-+_binary64` `associate-*l/_binary64`

Counts

3 → 408

Calls

3 calls:

28.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
20.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
9.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

series33.0ms (1%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
11.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
8.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

simplify203.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4990	10043
1	4990	10043

prune370.0ms (11%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	416	1	417
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	418	9	427

Merged error: 0b

Counts

427 → 9

Compiler

Compiled 9617 to 4948 computations (48.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.2b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
0.2b	(/.f64 PI.f64 (+.f64 b a))
0.3b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

rewrite95.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
76×	`times-frac_binary64`
37×	`associate-l_binary64`
35×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`associate-r_binary64`
21×	`difference-of-squares_binary64`
17×	`distribute-lft-out--_binary64`
16×	`frac-times_binary64`
12×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64` `div-inv_binary64`
10×	`associate-r/_binary64` `associate-l/_binary64`
8×	`flip3--_binary64` `flip--_binary64`
7×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-sub_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
4×	`pow-prod-down_binary64` `associate-/r*_binary64`
3×	`associate-/l*_binary64`
2×	`flip3-+_binary64` `unswap-sqr_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 179

Calls

4 calls:

33.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
30.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
14.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
6.0ms	(/.f64 PI.f64 (+.f64 b a))

series28.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
7.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))
6.0ms	(/.f64 PI.f64 (+.f64 b a))
3.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify108.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5242	4157

prune154.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	192	8	200

Merged error: 0b

Counts

200 → 8

Compiler

Compiled 4865 to 2489 computations (48.8% saved)

regimes69.0ms (2%)

Compiler: Compiled 298 to 218 computations (26.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	52	29
1	52	29

end0.0ms (0%)

sample1.1s (32.3%)

Algorithm

1×

intervals

Results

475.0ms	8000×	body	80	valid
22.0ms	378×	body	80	invalid

Compiler

Compiled 188 to 140 computations (25.5% saved)

Details

analyze229.0ms (6.8%)

sample26.0ms (0.8%)

simplify74.0ms (2.2%)

prune6.0ms (0.2%)

localize12.0ms (0.4%)

rewrite88.0ms (2.6%)

series32.0ms (1%)

simplify111.0ms (3.3%)

prune263.0ms (7.8%)

localize11.0ms (0.3%)

rewrite31.0ms (0.9%)

series19.0ms (0.6%)

simplify84.0ms (2.5%)

prune115.0ms (3.4%)

localize10.0ms (0.3%)

rewrite89.0ms (2.6%)

series33.0ms (1%)

simplify203.0ms (6.1%)

prune370.0ms (11%)

localize12.0ms (0.4%)

rewrite95.0ms (2.8%)

series28.0ms (0.8%)

simplify108.0ms (3.2%)

prune154.0ms (4.6%)

regimes69.0ms (2%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (32.3%)

Profiling