Details

analyze222.0ms (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)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
1.0ms	11×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify138.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

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

Merged error: 13.7b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
1.6b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.4b	(-.f64 (.f64 b b) (.f64 a a))
7.6b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite116.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64_425`
178×	`add-sqr-sqrt_binary64_441`
153×	`*-un-lft-identity_binary64_419`
121×	`add-cube-cbrt_binary64_454`
58×	`associate-l_binary64_360`
46×	`difference-of-squares_binary64_388`
40×	`cancel-sign-sub-inv_binary64_385`
22×	`div-inv_binary64_416`
19×	`associate-r_binary64_359`
18×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
14×	`distribute-rgt-in_binary64_369` `distribute-lft-out--_binary64_371` `distribute-lft-in_binary64_368`
13×	`associate-/l*_binary64_364`
8×	`add-log-exp_binary64_458`
6×	`flip3--_binary64_423` `flip--_binary64_394` `pow1_binary64_480` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`sub-neg_binary64_412` `associate-/r/_binary64_365` `associate-/r*_binary64_363`
3×	`unswap-sqr_binary64_387` `frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-*r/_binary64_361` `frac-sub_binary64_428`
2×	`diff-log_binary64_511`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `clear-num_binary64_418` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/l/_binary64_366`

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)))
15.0ms	(-.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))

series113.0ms (2.5%)

Counts

4 → 12

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)))
34.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
22.0ms	(-.f64 (.f64 b b) (.f64 a a))
11.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify123.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5154	7997

prune351.0ms (7.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	273	9	282
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	275	9	284

Merged error: 0.0b

Counts

284 → 9

Compiler

Compiled 8310 to 3974 computations (52.2% saved)

localize8.0ms (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))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64_425`
79×	`*-un-lft-identity_binary64_419`
60×	`add-exp-log_binary64_457`
51×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
39×	`add-cbrt-cube_binary64_455`
29×	`div-exp_binary64_470`
19×	`prod-exp_binary64_468`
17×	`cbrt-undiv_binary64_453`
14×	`distribute-lft-out_binary64_370` `associate-/l*_binary64_364`
10×	`cbrt-unprod_binary64_452`
7×	`div-inv_binary64_416`
6×	`1-exp_binary64_463`
5×	`associate-/r*_binary64_363`
2×	`clear-num_binary64_418` `add-log-exp_binary64_458` `associate-/r/_binary64_365` `frac-2neg_binary64_430` `pow1_binary64_480` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `associate-*l/_binary64_362` `flip-+_binary64_393`

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))

series73.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

44.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
29.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5189	2615

prune129.0ms (2.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	126	11	137

Merged error: 0b

Counts

137 → 11

Compiler

Compiled 2643 to 1338 computations (49.4% saved)

localize10.0ms (0.2%)

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)))

rewrite110.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

621×	`times-frac_binary64_425`
410×	`*-un-lft-identity_binary64_419`
278×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
202×	`add-exp-log_binary64_457`
120×	`div-exp_binary64_470`
71×	`associate-/r*_binary64_363`
66×	`distribute-lft-out_binary64_370`
62×	`add-cbrt-cube_binary64_455`
61×	`prod-exp_binary64_468`
35×	`1-exp_binary64_463`
31×	`cbrt-undiv_binary64_453`
28×	`div-inv_binary64_416`
15×	`rec-exp_binary64_469`
13×	`cbrt-unprod_binary64_452`
8×	`associate-/l*_binary64_364`
6×	`associate-/r/_binary64_365`
4×	`pow1_binary64_480`
3×	`clear-num_binary64_418` `add-log-exp_binary64_458` `frac-2neg_binary64_430` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `associate-*l/_binary64_362` `inv-pow_binary64_504` `pow-flip_binary64_493` `flip-+_binary64_393`

Counts

3 → 408

Calls

3 calls:

31.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
18.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
9.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

series113.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

42.0ms	(/.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)))
34.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

simplify157.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4963	10043
1	4963	10043

prune472.0ms (10.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	416	1	417
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	418	10	428

Merged error: 0b

Counts

428 → 10

Compiler

Compiled 9626 to 4969 computations (48.4% saved)

localize8.0ms (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)))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-exp-log_binary64_457`
42×	`add-cbrt-cube_binary64_455`
35×	`*-un-lft-identity_binary64_419`
29×	`prod-exp_binary64_468`
26×	`times-frac_binary64_425` `add-sqr-sqrt_binary64_441`
21×	`add-cube-cbrt_binary64_454`
20×	`div-exp_binary64_470`
18×	`associate-r_binary64_359`
16×	`cbrt-unprod_binary64_452`
12×	`cbrt-undiv_binary64_453`
7×	`distribute-lft-out_binary64_370`
6×	`1-exp_binary64_463`
5×	`associate-/r*_binary64_363` `pow1_binary64_480`
4×	`associate-/r/_binary64_365` `associate-/l*_binary64_364`
3×	`add-log-exp_binary64_458` `div-inv_binary64_416` `associate-l_binary64_360`
2×	`flip3-+_binary64_422` `clear-num_binary64_418` `unswap-sqr_binary64_387` `associate-*r/_binary64_361` `frac-2neg_binary64_430` `flip-+_binary64_393`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `-commutative_binary64_350` `associate-/l/_binary64_366`

Counts

3 → 106

Calls

3 calls:

12.0ms	(/.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))

series97.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

46.0ms	(/.f64 (.f64 (.f64 PI.f64 (/.f64 1/2 (+.f64 b a))) 1) (*.f64 a b))
29.0ms	(*.f64 PI.f64 (/.f64 1/2 (+.f64 b a)))
22.0ms	(/.f64 1/2 (+.f64 b a))

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4971	1615
1	4971	1615

prune94.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	117	8	125

Merged error: 0b

Counts

125 → 8

Compiler

Compiled 1912 to 955 computations (50.1% saved)

regimes314.0ms (6.9%)

Compiler: Compiled 3977 to 3057 computations (23.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	12	17

end0.0ms (0%)

sample1.6s (36%)

Algorithm

1×

intervals

Results

460.0ms	8000×	body	128	valid
18.0ms	328×	body	128	invalid

Compiler

Compiled 1322 to 1016 computations (23.1% saved)

Details

analyze222.0ms (4.9%)

sample25.0ms (0.5%)

simplify138.0ms (3%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite116.0ms (2.6%)

series113.0ms (2.5%)

simplify123.0ms (2.7%)

prune351.0ms (7.8%)

localize8.0ms (0.2%)

rewrite40.0ms (0.9%)

series73.0ms (1.6%)

simplify64.0ms (1.4%)

prune129.0ms (2.9%)

localize10.0ms (0.2%)

rewrite110.0ms (2.4%)

series113.0ms (2.5%)

simplify157.0ms (3.5%)

prune472.0ms (10.4%)

localize8.0ms (0.2%)

rewrite37.0ms (0.8%)

series97.0ms (2.1%)

simplify64.0ms (1.4%)

prune94.0ms (2.1%)

regimes314.0ms (6.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.6s (36%)

Profiling