Details

analyze279.0ms (3.7%)

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)

sample31.0ms (0.4%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify270.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5209	29

prune9.0ms (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: 12.8b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.4b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0b	(-.f64 (.f64 b b) (.f64 a a))
8.0b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite171.0ms (2.3%)

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:

93.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
18.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
11.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
5.0ms	(-.f64 (.f64 b b) (.f64 a a))

series286.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
84.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
59.0ms	(-.f64 (.f64 b b) (.f64 a a))
23.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify219.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4947	7997
1	4947	7997

prune549.0ms (7.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	271	11	282
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	273	11	284

Merged error: 0.0b

Counts

284 → 11

Compiler

Compiled 8393 to 4014 computations (52.2% saved)

localize18.0ms (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))
0.2b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite44.0ms (0.6%)

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:

18.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
11.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series183.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

109.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
74.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5176	2615

prune204.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	6	4	10
Picked	0	1	1
Done	0	0	0
Total	128	11	139

Merged error: 0b

Counts

139 → 11

Compiler

Compiled 2632 to 1324 computations (49.7% saved)

localize11.0ms (0.1%)

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))

rewrite245.0ms (3.3%)

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:

68.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
37.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
11.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

series283.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

126.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
89.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
67.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

simplify307.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4953	10043
1	4953	10043

prune632.0ms (8.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	415	2	417
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	419	9	428

Merged error: 0b

Counts

428 → 9

Compiler

Compiled 9585 to 4934 computations (48.5% saved)

localize10.0ms (0.1%)

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)))
0.2b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
0.6b	(/.f64 1 (*.f64 b a))

rewrite73.0ms (1%)

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:

30.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
10.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
6.0ms	(/.f64 1 (*.f64 b a))

series225.0ms (3%)

Counts

3 → 9

Calls

3 calls:

128.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
74.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
22.0ms	(/.f64 1 (*.f64 b a))

simplify150.0ms (2%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4935	3715
1	4935	3715

prune233.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	207	8	215

Merged error: 0b

Counts

215 → 8

Compiler

Compiled 3794 to 1961 computations (48.3% saved)

regimes540.0ms (7.2%)

Compiler: Compiled 4931 to 3567 computations (27.7% 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%)

sample2.4s (32%)

Algorithm

1×

intervals

Results

624.0ms	8000×	body	128	valid
35.0ms	413×	body	128	invalid

Compiler

Compiled 1640 to 1186 computations (27.7% saved)

Details

analyze279.0ms (3.7%)

sample31.0ms (0.4%)

simplify270.0ms (3.6%)

prune9.0ms (0.1%)

localize19.0ms (0.3%)

rewrite171.0ms (2.3%)

series286.0ms (3.8%)

simplify219.0ms (2.9%)

prune549.0ms (7.4%)

localize18.0ms (0.2%)

rewrite44.0ms (0.6%)

series183.0ms (2.5%)

simplify76.0ms (1%)

prune204.0ms (2.7%)

localize11.0ms (0.1%)

rewrite245.0ms (3.3%)

series283.0ms (3.8%)

simplify307.0ms (4.1%)

prune632.0ms (8.5%)

localize10.0ms (0.1%)

rewrite73.0ms (1%)

series225.0ms (3%)

simplify150.0ms (2%)

prune233.0ms (3.1%)

regimes540.0ms (7.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (32%)

Profiling