Details

analyze230.0ms (4.1%)

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)

sample23.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify216.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5209	29

prune6.0ms (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: 16.6b

Counts

2 → 2

Compiler

Compiled 99 to 79 computations (20.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.7b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.5b	(-.f64 (.f64 b b) (.f64 a a))
10.9b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite122.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64_773`
178×	`add-sqr-sqrt_binary64_789`
153×	`*-un-lft-identity_binary64_767`
121×	`add-cube-cbrt_binary64_802`
58×	`associate-l_binary64_708`
46×	`difference-of-squares_binary64_736`
40×	`cancel-sign-sub-inv_binary64_733`
22×	`div-inv_binary64_764`
19×	`associate-r_binary64_707`
18×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
14×	`distribute-rgt-in_binary64_717` `distribute-lft-out--_binary64_719` `distribute-lft-in_binary64_716`
13×	`associate-/l*_binary64_712`
8×	`add-log-exp_binary64_806`
6×	`cbrt-undiv_binary64_801` `pow1_binary64_828` `flip--_binary64_742` `div-exp_binary64_818` `flip3--_binary64_771`
4×	`associate-/r*_binary64_711` `associate-/r/_binary64_713` `sub-neg_binary64_760`
3×	`frac-times_binary64_777` `unswap-sqr_binary64_735` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `frac-sub_binary64_776` `associate-*r/_binary64_709`
2×	`diff-log_binary64_859`
1×	`frac-2neg_binary64_778` `associate-/l/_binary64_714` `-commutative_binary64_698` `associate-l/_binary64_710` `pow-prod-down_binary64_838` `clear-num_binary64_766`

Counts

4 → 270

Calls

4 calls:

51.0ms	(.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))

series249.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
77.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
48.0ms	(-.f64 (.f64 b b) (.f64 a a))
22.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify134.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4947	7997
1	4947	7997

prune669.0ms (11.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	275	7	282
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	277	7	284

Merged error: 0.0b

Counts

284 → 7

Compiler

Compiled 14247 to 8194 computations (42.5% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64_773`
79×	`*-un-lft-identity_binary64_767`
60×	`add-exp-log_binary64_805`
51×	`add-sqr-sqrt_binary64_789` `add-cube-cbrt_binary64_802`
39×	`add-cbrt-cube_binary64_803`
29×	`div-exp_binary64_818`
19×	`prod-exp_binary64_816`
17×	`cbrt-undiv_binary64_801`
14×	`distribute-lft-out_binary64_718` `associate-/l*_binary64_712`
10×	`cbrt-unprod_binary64_800`
7×	`div-inv_binary64_764`
6×	`1-exp_binary64_811`
5×	`associate-/r*_binary64_711`
2×	`frac-2neg_binary64_778` `associate-/l/_binary64_714` `associate-/r/_binary64_713` `pow1_binary64_828` `add-log-exp_binary64_806` `clear-num_binary64_766`
1×	`flip-+_binary64_741` `associate-*l/_binary64_710` `flip3-+_binary64_770`

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))

series150.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

89.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
61.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5176	2615

prune359.0ms (6.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	124	11	135

Merged error: 0.0b

Counts

135 → 11

Compiler

Compiled 7526 to 4838 computations (35.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite55.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

331×	`times-frac_binary64_773`
215×	`*-un-lft-identity_binary64_767`
135×	`add-sqr-sqrt_binary64_789` `add-cube-cbrt_binary64_802`
71×	`associate-/l*_binary64_712`
40×	`distribute-lft-out_binary64_718`
28×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
17×	`div-inv_binary64_764`
15×	`cbrt-undiv_binary64_801` `div-exp_binary64_818`
6×	`associate-/r/_binary64_713`
5×	`associate-/r*_binary64_711`
3×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816` `flip-+_binary64_741` `flip3-+_binary64_770`
2×	`frac-2neg_binary64_778` `associate-/l/_binary64_714` `pow1_binary64_828` `add-log-exp_binary64_806` `clear-num_binary64_766`

Counts

2 → 226

Calls

2 calls:

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

series148.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

87.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (*.f64 b a))
61.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify105.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4972	5513
1	4972	5513

prune376.0ms (6.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	227	5	232
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	232	11	243

Merged error: 0b

Counts

243 → 11

Compiler

Compiled 8111 to 4612 computations (43.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite202.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

1666×	`times-frac_binary64_773`
934×	`*-un-lft-identity_binary64_767`
646×	`add-sqr-sqrt_binary64_789` `add-cube-cbrt_binary64_802`
183×	`associate-/l*_binary64_712`
144×	`distribute-lft-out_binary64_718`
103×	`add-exp-log_binary64_805`
71×	`associate-/r*_binary64_711`
68×	`div-exp_binary64_818`
60×	`div-inv_binary64_764`
49×	`add-cbrt-cube_binary64_803`
29×	`cbrt-undiv_binary64_801`
14×	`associate-/r/_binary64_713`
10×	`prod-exp_binary64_816`
9×	`1-exp_binary64_811` `rec-exp_binary64_817`
4×	`cbrt-unprod_binary64_800` `pow1_binary64_828`
3×	`frac-2neg_binary64_778` `associate-/l/_binary64_714` `add-log-exp_binary64_806` `clear-num_binary64_766`
1×	`pow-flip_binary64_841` `flip-+_binary64_741` `flip3-+_binary64_770` `inv-pow_binary64_852`

Counts

3 → 734

Calls

3 calls:

49.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) (*.f64 b a))
18.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
9.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

series226.0ms (4%)

Counts

3 → 9

Calls

3 calls:

88.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) (*.f64 b a))
70.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
67.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

simplify233.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

743 → 743

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4998	20285
1	4998	20285

prune1.2s (20.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	741	2	743
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	744	10	754

Merged error: 0b

Counts

754 → 10

Compiler

Compiled 18655 to 9682 computations (48.1% saved)

regimes41.0ms (0.7%)

Compiler: Compiled 350 to 274 computations (21.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	12	17

end0.0ms (0%)

sample800.0ms (14.1%)

Algorithm

1×

intervals

Results

460.0ms	8000×	body	128	valid
18.0ms	324×	body	128	invalid

Compiler

Compiled 206 to 162 computations (21.4% saved)

Details

analyze230.0ms (4.1%)

sample23.0ms (0.4%)

simplify216.0ms (3.8%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite122.0ms (2.2%)

series249.0ms (4.4%)

simplify134.0ms (2.4%)

prune669.0ms (11.8%)

localize8.0ms (0.1%)

rewrite39.0ms (0.7%)

series150.0ms (2.6%)

simplify65.0ms (1.1%)

prune359.0ms (6.3%)

localize7.0ms (0.1%)

rewrite55.0ms (1%)

series148.0ms (2.6%)

simplify105.0ms (1.9%)

prune376.0ms (6.6%)

localize9.0ms (0.2%)

rewrite202.0ms (3.6%)

series226.0ms (4%)

simplify233.0ms (4.1%)

prune1.2s (20.9%)

regimes41.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample800.0ms (14.1%)

Profiling