Details

analyze219.0ms (4.9%)

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)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify138.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5241	29

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: 13.2b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.9b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
3.7b	(-.f64 (.f64 b b) (.f64 a a))
8.3b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite119.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64_766`
178×	`add-sqr-sqrt_binary64_782`
153×	`*-un-lft-identity_binary64_760`
121×	`add-cube-cbrt_binary64_795`
58×	`associate-l_binary64_701`
46×	`difference-of-squares_binary64_729`
40×	`cancel-sign-sub-inv_binary64_726`
22×	`div-inv_binary64_757`
19×	`associate-r_binary64_700`
18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `distribute-lft-out--_binary64_712`
13×	`associate-/l*_binary64_705`
8×	`add-log-exp_binary64_799`
6×	`cbrt-undiv_binary64_794` `div-exp_binary64_811` `pow1_binary64_821` `flip--_binary64_735` `flip3--_binary64_764`
4×	`associate-/r/_binary64_706` `associate-/r*_binary64_704` `sub-neg_binary64_753`
3×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `frac-times_binary64_770` `frac-sub_binary64_769` `associate-*r/_binary64_702` `cbrt-unprod_binary64_793`
2×	`diff-log_binary64_852`
1×	`frac-2neg_binary64_771` `associate-l/_binary64_703` `associate-/l/_binary64_707` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

4 → 270

Calls

4 calls:

53.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
16.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

series116.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
36.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
22.0ms	(-.f64 (.f64 b b) (.f64 a a))
11.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify121.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5154	7997

prune364.0ms (8.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	274	8	282
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	276	8	284

Merged error: 0.0b

Counts

284 → 8

Compiler

Compiled 8276 to 3941 computations (52.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64_766`
79×	`*-un-lft-identity_binary64_760`
60×	`add-exp-log_binary64_798`
51×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
39×	`add-cbrt-cube_binary64_796`
29×	`div-exp_binary64_811`
19×	`prod-exp_binary64_809`
17×	`cbrt-undiv_binary64_794`
14×	`distribute-lft-out_binary64_711` `associate-/l*_binary64_705`
10×	`cbrt-unprod_binary64_793`
7×	`div-inv_binary64_757`
6×	`1-exp_binary64_804`
5×	`associate-/r*_binary64_704`
2×	`frac-2neg_binary64_771` `associate-/r/_binary64_706` `associate-/l/_binary64_707` `add-log-exp_binary64_799` `pow1_binary64_821` `clear-num_binary64_759`
1×	`associate-*l/_binary64_703` `flip3-+_binary64_763` `flip-+_binary64_734`

Counts

2 → 122

Calls

2 calls:

15.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series78.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

47.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
30.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify65.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5189	2615

prune124.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	123	5	128
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Merged error: 0b

Counts

136 → 8

Compiler

Compiled 2582 to 1293 computations (49.9% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite115.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

621×	`times-frac_binary64_766`
410×	`*-un-lft-identity_binary64_760`
278×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
202×	`add-exp-log_binary64_798`
120×	`div-exp_binary64_811`
71×	`associate-/r*_binary64_704`
66×	`distribute-lft-out_binary64_711`
62×	`add-cbrt-cube_binary64_796`
61×	`prod-exp_binary64_809`
35×	`1-exp_binary64_804`
31×	`cbrt-undiv_binary64_794`
28×	`div-inv_binary64_757`
15×	`rec-exp_binary64_810`
13×	`cbrt-unprod_binary64_793`
8×	`associate-/l*_binary64_705`
6×	`associate-/r/_binary64_706`
4×	`pow1_binary64_821`
3×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `add-log-exp_binary64_799` `clear-num_binary64_759`
1×	`associate-*l/_binary64_703` `flip3-+_binary64_763` `inv-pow_binary64_845` `flip-+_binary64_734` `pow-flip_binary64_834`

Counts

3 → 408

Calls

3 calls:

29.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
19.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
9.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

series114.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

44.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
40.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
29.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

simplify156.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4963	10043
1	4963	10043

prune491.0ms (10.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	417	0	417
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	417	8	425

Merged error: 0b

Counts

425 → 8

Compiler

Compiled 9580 to 4928 computations (48.6% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
0.8b	(/.f64 1 (*.f64 b a))

rewrite52.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

215×	`add-exp-log_binary64_798`
115×	`prod-exp_binary64_809`
103×	`times-frac_binary64_766`
84×	`*-un-lft-identity_binary64_760`
77×	`div-exp_binary64_811`
67×	`add-cbrt-cube_binary64_796`
56×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
37×	`1-exp_binary64_804`
26×	`cbrt-unprod_binary64_793`
22×	`cbrt-undiv_binary64_794`
16×	`associate-/l*_binary64_705` `rec-exp_binary64_810`
14×	`distribute-lft-out_binary64_711`
11×	`pow1_binary64_821`
8×	`div-inv_binary64_757`
7×	`associate-r_binary64_700`
5×	`associate-/r*_binary64_704`
4×	`pow-prod-down_binary64_831`
3×	`associate-*l/_binary64_703` `add-log-exp_binary64_799`
2×	`frac-2neg_binary64_771` `associate-/r/_binary64_706` `clear-num_binary64_759` `pow-flip_binary64_834`
1×	`flip3-+_binary64_763` `associate-/l/_binary64_707` `inv-pow_binary64_845` `flip-+_binary64_734` `frac-times_binary64_770` `associate-l_binary64_701` `associate-r/_binary64_702` `un-div-inv_binary64_758` `-commutative_binary64_691`

Counts

3 → 197

Calls

3 calls:

19.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
8.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
4.0ms	(/.f64 1 (*.f64 b a))

series84.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
29.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
10.0ms	(/.f64 1 (*.f64 b a))

simplify103.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4956	3715
1	4956	3715

prune172.0ms (3.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	206	8	214

Merged error: 0b

Counts

214 → 8

Compiler

Compiled 3794 to 1961 computations (48.3% saved)

regimes277.0ms (6.2%)

Compiler: Compiled 3530 to 2598 computations (26.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	12	17

end0.0ms (0%)

sample1.5s (33%)

Algorithm

1×

intervals

Results

453.0ms	8000×	body	128	valid
19.0ms	336×	body	128	invalid

Compiler

Compiled 1173 to 863 computations (26.4% saved)

Details

analyze219.0ms (4.9%)

sample22.0ms (0.5%)

simplify138.0ms (3.1%)

prune4.0ms (0.1%)

localize11.0ms (0.3%)

rewrite119.0ms (2.6%)

series116.0ms (2.6%)

simplify121.0ms (2.7%)

prune364.0ms (8.1%)

localize8.0ms (0.2%)

rewrite35.0ms (0.8%)

series78.0ms (1.7%)

simplify65.0ms (1.5%)

prune124.0ms (2.7%)

localize12.0ms (0.3%)

rewrite115.0ms (2.6%)

series114.0ms (2.5%)

simplify156.0ms (3.5%)

prune491.0ms (10.9%)

localize13.0ms (0.3%)

rewrite52.0ms (1.2%)

series84.0ms (1.9%)

simplify103.0ms (2.3%)

prune172.0ms (3.8%)

regimes277.0ms (6.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.5s (33%)

Profiling