Details

analyze297.0ms (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)

sample23.0ms (0.4%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify170.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

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

Error

12.1b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize24.0ms (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)))
3.5b	(-.f64 (.f64 b b) (.f64 a a))
7.8b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite162.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64_84`
178×	`add-sqr-sqrt_binary64_100`
153×	`*-un-lft-identity_binary64_78`
121×	`add-cube-cbrt_binary64_113`
58×	`associate-l_binary64_19`
46×	`difference-of-squares_binary64_47`
40×	`cancel-sign-sub-inv_binary64_44`
22×	`div-inv_binary64_75`
19×	`associate-r_binary64_18`
18×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
14×	`distribute-lft-in_binary64_27` `distribute-lft-out--_binary64_30` `distribute-rgt-in_binary64_28`
13×	`associate-/l*_binary64_23`
8×	`add-log-exp_binary64_117`
6×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip3--_binary64_82` `flip--_binary64_53` `pow1_binary64_139`
4×	`associate-/r*_binary64_22` `associate-/r/_binary64_24` `sub-neg_binary64_71`
3×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `frac-sub_binary64_87` `frac-times_binary64_88` `unswap-sqr_binary64_46` `associate-*r/_binary64_20`
2×	`diff-log_binary64_170`
1×	`-commutative_binary64_9` `frac-2neg_binary64_89` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `clear-num_binary64_77` `associate-/l/_binary64_25`

Counts

4 → 270

Calls

4 calls:

52.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
29.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
13.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

series165.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
35.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
25.0ms	(-.f64 (.f64 b b) (.f64 a a))
11.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify126.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5154	7997

prune518.0ms (8.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	272	10	282
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	274	10	284

Error

0.0b

Counts

284 → 10

Compiler

Compiled 8349 to 3998 computations (52.1% saved)

localize8.0ms (0.1%)

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))

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64_84`
79×	`*-un-lft-identity_binary64_78`
60×	`add-exp-log_binary64_116`
51×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
39×	`add-cbrt-cube_binary64_114`
29×	`div-exp_binary64_129`
19×	`prod-exp_binary64_127`
17×	`cbrt-undiv_binary64_112`
14×	`associate-/l*_binary64_23` `distribute-lft-out_binary64_29`
10×	`cbrt-unprod_binary64_111`
7×	`div-inv_binary64_75`
6×	`1-exp_binary64_122`
5×	`associate-/r*_binary64_22`
2×	`add-log-exp_binary64_117` `frac-2neg_binary64_89` `associate-/r/_binary64_24` `clear-num_binary64_77` `associate-/l/_binary64_25` `pow1_binary64_139`
1×	`flip-+_binary64_52` `associate-*l/_binary64_21` `flip3-+_binary64_81`

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))

series98.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

66.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
32.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5189	2615

prune154.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	128	10	138

Error

Counts

138 → 10

Compiler

Compiled 2649 to 1340 computations (49.4% saved)

localize15.0ms (0.3%)

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)))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-exp-log_binary64_116`
42×	`add-cbrt-cube_binary64_114`
35×	`*-un-lft-identity_binary64_78`
29×	`prod-exp_binary64_127`
26×	`add-sqr-sqrt_binary64_100` `times-frac_binary64_84`
21×	`add-cube-cbrt_binary64_113`
20×	`div-exp_binary64_129`
18×	`associate-r_binary64_18`
16×	`cbrt-unprod_binary64_111`
12×	`cbrt-undiv_binary64_112`
7×	`distribute-lft-out_binary64_29`
6×	`1-exp_binary64_122`
5×	`associate-/r*_binary64_22` `pow1_binary64_139`
4×	`associate-/l*_binary64_23` `associate-/r/_binary64_24`
3×	`associate-l_binary64_19` `add-log-exp_binary64_117` `div-inv_binary64_75`
2×	`flip-+_binary64_52` `frac-2neg_binary64_89` `unswap-sqr_binary64_46` `associate-*r/_binary64_20` `clear-num_binary64_77` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-/l/_binary64_25`

Counts

3 → 106

Calls

3 calls:

12.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
10.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
5.0ms	(/.f64 1/2 (+.f64 b a))

series155.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

57.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
56.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
42.0ms	(/.f64 1/2 (+.f64 b a))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4971	1615
1	4971	1615

prune197.0ms (3.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	115	10	125

Error

Counts

125 → 10

Compiler

Compiled 2100 to 1097 computations (47.8% saved)

localize23.0ms (0.4%)

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))

rewrite67.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`add-exp-log_binary64_116`
73×	`add-cbrt-cube_binary64_114`
61×	`prod-exp_binary64_127` `*-un-lft-identity_binary64_78`
49×	`times-frac_binary64_84`
35×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
34×	`cbrt-unprod_binary64_111`
33×	`div-exp_binary64_129`
30×	`associate-r_binary64_18`
27×	`sqrt-prod_binary64_94`
19×	`cbrt-undiv_binary64_112`
13×	`distribute-lft-out_binary64_29`
10×	`1-exp_binary64_122`
8×	`pow1_binary64_139`
7×	`associate-/l*_binary64_23`
5×	`associate-/r*_binary64_22`
4×	`associate-/r/_binary64_24`
3×	`add-log-exp_binary64_117` `div-inv_binary64_75` `pow-prod-down_binary64_149`
2×	`flip-+_binary64_52` `frac-2neg_binary64_89` `associate-*r/_binary64_20` `clear-num_binary64_77` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `associate-l_binary64_19` `associate-l/_binary64_21` `associate-/l/_binary64_25`

Counts

3 → 146

Calls

3 calls:

21.0ms

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

17.0ms

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

13.0ms

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

series308.0ms (5.1%)

Counts

3 → 9

Calls

3 calls:

133.0ms

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

111.0ms

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

63.0ms

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

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5724	2510

prune275.0ms (4.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	152	3	155
Fresh	5	3	8
Picked	1	0	1
Done	0	1	1
Total	158	7	165

Error

Counts

165 → 7

Compiler

Compiled 2990 to 1680 computations (43.8% saved)

regimes491.0ms (8.1%)

Accuracy

Total 0.2b remaining (99.9%)

Threshold costs 0.2b (99.9%)

Compiler

Compiled 4439 to 3309 computations (25.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	17
1	16	17

end0.0ms (0%)

sample2.4s (40.2%)

Algorithm

1×

intervals

Results

651.0ms	8000×	body	128	valid
32.0ms	372×	body	128	invalid

Compiler

Compiled 1476 to 1100 computations (25.5% saved)

Details

analyze297.0ms (4.9%)

sample23.0ms (0.4%)

simplify170.0ms (2.8%)

prune4.0ms (0.1%)

localize24.0ms (0.4%)

rewrite162.0ms (2.7%)

series165.0ms (2.7%)

simplify126.0ms (2.1%)

prune518.0ms (8.5%)

localize8.0ms (0.1%)

rewrite50.0ms (0.8%)

series98.0ms (1.6%)

simplify91.0ms (1.5%)

prune154.0ms (2.5%)

localize15.0ms (0.3%)

rewrite45.0ms (0.7%)

series155.0ms (2.5%)

simplify91.0ms (1.5%)

prune197.0ms (3.2%)

localize23.0ms (0.4%)

rewrite67.0ms (1.1%)

series308.0ms (5.1%)

simplify80.0ms (1.3%)

prune275.0ms (4.5%)

regimes491.0ms (8.1%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.4s (40.2%)

Profiling