Details

analyze224.0ms (4.5%)

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)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify209.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5209	29

prune5.0ms (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: 14.4b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize16.0ms (0.3%)

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)))
4.1b	(-.f64 (.f64 b b) (.f64 a a))
9.6b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite117.0ms (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:

48.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
19.0ms	(-.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))

series246.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
71.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
52.0ms	(-.f64 (.f64 b b) (.f64 a a))
21.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify137.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4947	7997
1	4947	7997

prune393.0ms (7.8%)

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 8326 to 3977 computations (52.2% saved)

localize9.0ms (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))

rewrite39.0ms (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:

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))

series144.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

80.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
64.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5176	2615

prune125.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	128	8	136

Merged error: 0b

Counts

136 → 8

Compiler

Compiled 2549 to 1272 computations (50.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-exp-log_binary64_798`
42×	`add-cbrt-cube_binary64_796`
35×	`*-un-lft-identity_binary64_760`
29×	`prod-exp_binary64_809`
26×	`times-frac_binary64_766` `add-sqr-sqrt_binary64_782`
21×	`add-cube-cbrt_binary64_795`
20×	`div-exp_binary64_811`
18×	`associate-r_binary64_700`
16×	`cbrt-unprod_binary64_793`
12×	`cbrt-undiv_binary64_794`
7×	`distribute-lft-out_binary64_711`
6×	`1-exp_binary64_804`
5×	`associate-/r*_binary64_704` `pow1_binary64_821`
4×	`associate-/r/_binary64_706` `associate-/l*_binary64_705`
3×	`add-log-exp_binary64_799` `div-inv_binary64_757` `associate-l_binary64_701`
2×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-*r/_binary64_702` `clear-num_binary64_759`
1×	`associate-l/_binary64_703` `associate-/l/_binary64_707` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

3 → 106

Calls

3 calls:

13.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
11.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
5.0ms	(/.f64 1/2 (+.f64 b a))

series196.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

88.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
57.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
50.0ms	(/.f64 1/2 (+.f64 b a))

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4975	1614
1	4975	1614

prune96.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	115	8	123

Merged error: 0b

Counts

123 → 8

Compiler

Compiled 2015 to 1037 computations (48.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b

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

0.3b

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

0.5b

(/.f64 (sqrt.f64 1/2) (+.f64 b a))

rewrite62.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`add-exp-log_binary64_798`
73×	`add-cbrt-cube_binary64_796`
61×	`*-un-lft-identity_binary64_760` `prod-exp_binary64_809`
49×	`times-frac_binary64_766`
35×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
34×	`cbrt-unprod_binary64_793`
33×	`div-exp_binary64_811`
30×	`associate-r_binary64_700`
27×	`sqrt-prod_binary64_776`
19×	`cbrt-undiv_binary64_794`
13×	`distribute-lft-out_binary64_711`
10×	`1-exp_binary64_804`
8×	`pow1_binary64_821`
7×	`associate-/l*_binary64_705`
5×	`associate-/r*_binary64_704`
4×	`associate-/r/_binary64_706`
3×	`add-log-exp_binary64_799` `div-inv_binary64_757` `pow-prod-down_binary64_831`
2×	`frac-2neg_binary64_771` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-*r/_binary64_702` `clear-num_binary64_759`
1×	`associate-l/_binary64_703` `associate-/l/_binary64_707` `associate-l_binary64_701` `-commutative_binary64_691`

Counts

3 → 146

Calls

3 calls:

18.0ms

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

15.0ms

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

7.0ms

(/.f64 (sqrt.f64 1/2) (+.f64 b a))

series459.0ms (9.2%)

Counts

3 → 9

Calls

3 calls:

210.0ms

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

176.0ms

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

73.0ms

(/.f64 (sqrt.f64 1/2) (+.f64 b a))

simplify72.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5656	2510

prune146.0ms (2.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	155	8	163

Merged error: 0b

Counts

163 → 8

Compiler

Compiled 2990 to 1680 computations (43.8% saved)

regimes360.0ms (7.2%)

Compiler: Compiled 4691 to 3309 computations (29.5% 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%)

sample1.7s (34.5%)

Algorithm

1×

intervals

Results

465.0ms	8000×	body	128	valid
20.0ms	351×	body	128	invalid

Compiler

Compiled 1560 to 1100 computations (29.5% saved)

Details

analyze224.0ms (4.5%)

sample25.0ms (0.5%)

simplify209.0ms (4.2%)

prune5.0ms (0.1%)

localize16.0ms (0.3%)

rewrite117.0ms (2.3%)

series246.0ms (4.9%)

simplify137.0ms (2.7%)

prune393.0ms (7.8%)

localize9.0ms (0.2%)

rewrite39.0ms (0.8%)

series144.0ms (2.9%)

simplify65.0ms (1.3%)

prune125.0ms (2.5%)

localize9.0ms (0.2%)

rewrite40.0ms (0.8%)

series196.0ms (3.9%)

simplify81.0ms (1.6%)

prune96.0ms (1.9%)

localize11.0ms (0.2%)

rewrite62.0ms (1.2%)

series459.0ms (9.2%)

simplify72.0ms (1.4%)

prune146.0ms (2.9%)

regimes360.0ms (7.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (34.5%)

Profiling