Details

analyze228.0ms (6%)

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 (0.6%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify55.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5000	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: 13.5b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize15.0ms (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)))
4.4b	(-.f64 (.f64 b b) (.f64 a a))
8.5b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite110.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

224×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
132×	`*-un-lft-identity_binary64`
100×	`add-cube-cbrt_binary64`
58×	`associate-l_binary64`
46×	`difference-of-squares_binary64`
19×	`associate-r_binary64` `div-inv_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`distribute-lft-out--_binary64`
13×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
4×	`associate-/r*_binary64` `sub-neg_binary64` `associate-/r/_binary64`
3×	`cbrt-unprod_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-sub_binary64` `frac-times_binary64`
2×	`diff-log_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 230

Calls

4 calls:

47.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
20.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
10.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

series231.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

98.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
65.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
47.0ms	(-.f64 (.f64 b b) (.f64 a a))
21.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify92.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5035	6697

prune352.0ms (9.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	233	9	242
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	235	9	244

Merged error: 0.0b

Counts

244 → 9

Compiler

Compiled 7255 to 3550 computations (51.1% 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))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64`
79×	`*-un-lft-identity_binary64`
60×	`add-exp-log_binary64`
51×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
39×	`add-cbrt-cube_binary64`
29×	`div-exp_binary64`
19×	`prod-exp_binary64`
17×	`cbrt-undiv_binary64`
14×	`distribute-lft-out_binary64` `associate-/l*_binary64`
10×	`cbrt-unprod_binary64`
7×	`div-inv_binary64`
6×	`1-exp_binary64`
5×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`

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))

series155.0ms (4.1%)

Counts

2 → 6

Calls

2 calls:

90.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
65.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify66.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5133	2615

prune133.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	130	7	137

Merged error: 0b

Counts

137 → 7

Compiler

Compiled 2595 to 1291 computations (50.3% saved)

localize10.0ms (0.3%)

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

rewrite120.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

621×	`times-frac_binary64`
410×	`*-un-lft-identity_binary64`
278×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
202×	`add-exp-log_binary64`
120×	`div-exp_binary64`
71×	`associate-/r*_binary64`
66×	`distribute-lft-out_binary64`
62×	`add-cbrt-cube_binary64`
61×	`prod-exp_binary64`
35×	`1-exp_binary64`
31×	`cbrt-undiv_binary64`
28×	`div-inv_binary64`
15×	`rec-exp_binary64`
13×	`cbrt-unprod_binary64`
8×	`associate-/l*_binary64`
6×	`associate-/r/_binary64`
4×	`pow1_binary64`
3×	`associate-/l/_binary64` `add-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `inv-pow_binary64` `pow-flip_binary64` `flip-+_binary64` `associate-*l/_binary64`

Counts

3 → 408

Calls

3 calls:

30.0ms	(/.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))

series220.0ms (5.8%)

Counts

3 → 9

Calls

3 calls:

87.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
70.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
63.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

simplify163.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4988	10043
1	4988	10043

prune512.0ms (13.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	416	1	417
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	417	7	424

Merged error: 0b

Counts

424 → 7

Compiler

Compiled 9588 to 4928 computations (48.6% 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))
0.4b	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-exp-log_binary64`
42×	`add-cbrt-cube_binary64`
35×	`*-un-lft-identity_binary64`
29×	`prod-exp_binary64`
26×	`add-sqr-sqrt_binary64` `times-frac_binary64`
21×	`add-cube-cbrt_binary64`
20×	`div-exp_binary64`
18×	`associate-r_binary64`
16×	`cbrt-unprod_binary64`
12×	`cbrt-undiv_binary64`
7×	`distribute-lft-out_binary64`
6×	`1-exp_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
4×	`associate-/r/_binary64` `associate-/l*_binary64`
3×	`add-log-exp_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-l/_binary64` `-commutative_binary64`

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)))
6.0ms	(/.f64 1/2 (+.f64 b a))

series190.0ms (5%)

Counts

3 → 9

Calls

3 calls:

80.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
66.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
44.0ms	(/.f64 1/2 (+.f64 b a))

simplify83.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4966	1614
1	4966	1614

prune95.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	115	7	122

Merged error: 0b

Counts

122 → 7

Compiler

Compiled 1911 to 953 computations (50.1% saved)

regimes34.0ms (0.9%)

Compiler: Compiled 280 to 214 computations (23.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	20
1	17	20

end0.0ms (0%)

sample793.0ms (20.9%)

Algorithm

1×

intervals

Results

474.0ms	8000×	body	128	valid
20.0ms	348×	body	128	invalid

Compiler

Compiled 173 to 134 computations (22.5% saved)

Details

analyze228.0ms (6%)

sample23.0ms (0.6%)

simplify55.0ms (1.4%)

prune5.0ms (0.1%)

localize15.0ms (0.4%)

rewrite110.0ms (2.9%)

series231.0ms (6.1%)

simplify92.0ms (2.4%)

prune352.0ms (9.3%)

localize9.0ms (0.2%)

rewrite39.0ms (1%)

series155.0ms (4.1%)

simplify66.0ms (1.7%)

prune133.0ms (3.5%)

localize10.0ms (0.3%)

rewrite120.0ms (3.2%)

series220.0ms (5.8%)

simplify163.0ms (4.3%)

prune512.0ms (13.5%)

localize9.0ms (0.2%)

rewrite40.0ms (1.1%)

series190.0ms (5%)

simplify83.0ms (2.2%)

prune95.0ms (2.5%)

regimes34.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample793.0ms (20.9%)

Profiling