Details

analyze217.0ms (4.1%)

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

14.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify141.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5241	29

prune7.0ms (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: 14.0b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 PI.f64 2) (/.f64 1 (-.f64 (.f64 b b) (*.f64 a a))))
0.6b	(/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))
4.6b	(-.f64 (.f64 b b) (.f64 a a))
8.3b	(.f64 (.f64 (/.f64 PI.f64 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite80.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64_441`
76×	`times-frac_binary64_425`
63×	`*-un-lft-identity_binary64_419`
62×	`add-exp-log_binary64_457`
45×	`add-cube-cbrt_binary64_454`
37×	`associate-r_binary64_359`
36×	`add-cbrt-cube_binary64_455`
27×	`cancel-sign-sub-inv_binary64_385`
25×	`prod-exp_binary64_468`
18×	`div-exp_binary64_470`
17×	`difference-of-squares_binary64_388` `frac-times_binary64_429`
14×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360`
13×	`cbrt-unprod_binary64_452`
12×	`pow1_binary64_480`
9×	`associate-*l/_binary64_362` `div-inv_binary64_416` `cbrt-undiv_binary64_453`
8×	`flip3--_binary64_423` `associate-*r/_binary64_361` `flip--_binary64_394`
7×	`distribute-lft-out--_binary64_371`
6×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387`
5×	`1-exp_binary64_463` `rec-exp_binary64_469` `un-div-inv_binary64_417` `frac-sub_binary64_428`
4×	`pow-prod-down_binary64_490` `associate-/r/_binary64_365` `associate-/r*_binary64_363`
3×	`sub-neg_binary64_412` `associate-/l*_binary64_364`
2×	`*-commutative_binary64_350`
1×	`clear-num_binary64_418` `inv-pow_binary64_504` `frac-2neg_binary64_430` `pow-flip_binary64_493` `diff-log_binary64_511`

Counts

4 → 203

Calls

4 calls:

29.0ms	(.f64 (.f64 (/.f64 PI.f64 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
16.0ms	(.f64 (/.f64 PI.f64 2) (/.f64 1 (-.f64 (.f64 b b) (*.f64 a a))))
6.0ms	(/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

series130.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(.f64 (.f64 (/.f64 PI.f64 2) (/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
36.0ms	(.f64 (/.f64 PI.f64 2) (/.f64 1 (-.f64 (.f64 b b) (*.f64 a a))))
25.0ms	(/.f64 1 (-.f64 (.f64 b b) (.f64 a a)))
22.0ms	(-.f64 (.f64 b b) (.f64 a a))

simplify122.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4971	5432
1	4971	5432

prune286.0ms (5.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	205	10	215
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	207	10	217

Merged error: 8.2b

Counts

217 → 10

Compiler

Compiled 5931 to 2954 computations (50.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.1b	(/.f64 (/.f64 1 (+.f64 b a)) (-.f64 b a))
0.2b	(*.f64 (/.f64 PI.f64 2) (/.f64 (/.f64 1 (+.f64 b a)) (-.f64 b a)))
8.3b	(.f64 (.f64 (/.f64 PI.f64 2) (/.f64 (/.f64 1 (+.f64 b a)) (-.f64 b a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite168.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

398×	`times-frac_binary64_425`
337×	`*-un-lft-identity_binary64_419`
313×	`add-sqr-sqrt_binary64_441`
163×	`add-cube-cbrt_binary64_454`
115×	`associate-r_binary64_359`
95×	`add-exp-log_binary64_457`
59×	`add-cbrt-cube_binary64_455`
55×	`difference-of-squares_binary64_388`
51×	`distribute-lft-out--_binary64_371`
40×	`div-exp_binary64_470`
39×	`cancel-sign-sub-inv_binary64_385`
33×	`distribute-lft-out_binary64_370`
31×	`prod-exp_binary64_468`
26×	`associate-/r/_binary64_365`
25×	`div-inv_binary64_416`
21×	`cbrt-undiv_binary64_453`
19×	`cbrt-unprod_binary64_452`
18×	`associate-/l*_binary64_364`
14×	`distribute-rgt-in_binary64_369` `frac-times_binary64_429` `distribute-lft-in_binary64_368` `associate-l_binary64_360`
11×	`flip3-+_binary64_422` `flip-+_binary64_393` `pow1_binary64_480`
8×	`associate-l/_binary64_362` `unswap-sqr_binary64_387` `associate-r/_binary64_361`
7×	`flip3--_binary64_423` `flip--_binary64_394`
6×	`add-log-exp_binary64_458`
5×	`1-exp_binary64_463` `rec-exp_binary64_469` `associate-/r*_binary64_363` `frac-sub_binary64_428`
4×	`pow-prod-down_binary64_490`
3×	`sub-neg_binary64_412`
2×	`*-commutative_binary64_350`
1×	`clear-num_binary64_418` `frac-2neg_binary64_430` `diff-log_binary64_511` `associate-/l/_binary64_366`

Counts

4 → 409

Calls

4 calls:

47.0ms	(*.f64 (/.f64 PI.f64 2) (/.f64 (/.f64 1 (+.f64 b a)) (-.f64 b a)))
37.0ms	(.f64 (.f64 (/.f64 PI.f64 2) (/.f64 (/.f64 1 (+.f64 b a)) (-.f64 b a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
15.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
12.0ms	(/.f64 (/.f64 1 (+.f64 b a)) (-.f64 b a))

series134.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(.f64 (.f64 (/.f64 PI.f64 2) (/.f64 (/.f64 1 (+.f64 b a)) (-.f64 b a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
39.0ms	(*.f64 (/.f64 PI.f64 2) (/.f64 (/.f64 1 (+.f64 b a)) (-.f64 b a)))
34.0ms	(/.f64 (/.f64 1 (+.f64 b a)) (-.f64 b a))
11.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify142.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

421 → 421

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4992	10833
1	4992	10833

prune627.0ms (11.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	416	5	421
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	422	9	431

Merged error: 0.0b

Counts

431 → 9

Compiler

Compiled 12687 to 6501 computations (48.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite91.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64_441`
79×	`*-un-lft-identity_binary64_419`
71×	`times-frac_binary64_425`
33×	`add-cube-cbrt_binary64_454`
32×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
19×	`associate-l_binary64_360`
18×	`difference-of-squares_binary64_388` `associate-r_binary64_359`
14×	`distribute-lft-out--_binary64_371`
13×	`cancel-sign-sub-inv_binary64_385`
12×	`div-inv_binary64_416`
10×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
9×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
7×	`distribute-lft-out_binary64_370` `associate-/l/_binary64_366`
6×	`associate-*l/_binary64_362` `add-log-exp_binary64_458` `frac-times_binary64_429` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip--_binary64_394` `pow1_binary64_480`
5×	`associate-/r*_binary64_363` `frac-sub_binary64_428`
4×	`associate-r/_binary64_361` `associate-/l_binary64_364`
2×	`flip3-+_binary64_422` `clear-num_binary64_418` `unswap-sqr_binary64_387` `frac-2neg_binary64_430` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `*-commutative_binary64_350` `diff-log_binary64_511`

Counts

4 → 167

Calls

4 calls:

30.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 PI.f64 (+.f64 b a)))
25.0ms	(/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 PI.f64 (+.f64 b a))) (.f64 2 (-.f64 b a)))
14.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
5.0ms	(/.f64 PI.f64 (+.f64 b a))

series132.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 PI.f64 (+.f64 b a)))
48.0ms	(/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 PI.f64 (+.f64 b a))) (.f64 2 (-.f64 b a)))
22.0ms	(/.f64 PI.f64 (+.f64 b a))
10.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5006	3526

prune211.0ms (3.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	174	5	179
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	179	9	188

Merged error: 0.0b

Counts

188 → 9

Compiler

Compiled 4650 to 2387 computations (48.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite125.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

217×	`times-frac_binary64_425`
174×	`*-un-lft-identity_binary64_419`
144×	`add-sqr-sqrt_binary64_441`
106×	`add-cube-cbrt_binary64_454`
100×	`add-exp-log_binary64_457`
53×	`associate-r_binary64_359`
52×	`add-cbrt-cube_binary64_455`
45×	`div-exp_binary64_470`
29×	`prod-exp_binary64_468`
25×	`distribute-lft-out_binary64_370`
21×	`cbrt-undiv_binary64_453`
20×	`associate-/r*_binary64_363`
19×	`associate-l_binary64_360`
15×	`div-inv_binary64_416`
13×	`cbrt-unprod_binary64_452`
10×	`associate-/l/_binary64_366`
9×	`difference-of-squares_binary64_388`
8×	`1-exp_binary64_463` `rec-exp_binary64_469` `associate-/l*_binary64_364`
7×	`distribute-lft-out--_binary64_371` `pow1_binary64_480`
6×	`associate-*l/_binary64_362` `frac-times_binary64_429`
5×	`unswap-sqr_binary64_387` `flip3--_binary64_423` `flip--_binary64_394`
4×	`add-log-exp_binary64_458` `associate-*r/_binary64_361` `associate-/r/_binary64_365` `frac-sub_binary64_428`
3×	`clear-num_binary64_418` `frac-2neg_binary64_430`
2×	`un-div-inv_binary64_417`
1×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `inv-pow_binary64_504` `*-commutative_binary64_350` `pow-flip_binary64_493` `flip-+_binary64_393`

Counts

4 → 272

Calls

4 calls:

46.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1 (/.f64 (+.f64 a b) PI.f64)))
30.0ms	(/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1 (/.f64 (+.f64 a b) PI.f64))) (.f64 2 (-.f64 b a)))
8.0ms	(/.f64 1 (/.f64 (+.f64 a b) PI.f64))
5.0ms	(/.f64 (+.f64 a b) PI.f64)

series151.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(/.f64 (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1 (/.f64 (+.f64 a b) PI.f64))) (.f64 2 (-.f64 b a)))
47.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1 (/.f64 (+.f64 a b) PI.f64)))
27.0ms	(/.f64 (+.f64 a b) PI.f64)
23.0ms	(/.f64 1 (/.f64 (+.f64 a b) PI.f64))

simplify108.0ms (2%)

Algorithm

1×	egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5912	6132

prune360.0ms (6.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	283	1	284
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	283	10	293

Merged error: 0.0b

Counts

293 → 10

Compiler

Compiled 7648 to 3761 computations (50.8% saved)

regimes314.0ms (5.9%)

Compiler: Compiled 4322 to 3207 computations (25.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	29
1	50	29

end0.0ms (0%)

sample1.6s (30.8%)

Algorithm

1×

intervals

Results

462.0ms	8000×	body	128	valid
22.0ms	390×	body	128	invalid

Compiler

Compiled 1445 to 1072 computations (25.8% saved)

Details

analyze217.0ms (4.1%)

sample23.0ms (0.4%)

simplify141.0ms (2.6%)

prune7.0ms (0.1%)

localize13.0ms (0.2%)

rewrite80.0ms (1.5%)

series130.0ms (2.4%)

simplify122.0ms (2.3%)

prune286.0ms (5.3%)

localize13.0ms (0.2%)

rewrite168.0ms (3.1%)

series134.0ms (2.5%)

simplify142.0ms (2.7%)

prune627.0ms (11.7%)

localize11.0ms (0.2%)

rewrite91.0ms (1.7%)

series132.0ms (2.5%)

simplify82.0ms (1.5%)

prune211.0ms (3.9%)

localize13.0ms (0.2%)

rewrite125.0ms (2.3%)

series151.0ms (2.8%)

simplify108.0ms (2%)

prune360.0ms (6.7%)

regimes314.0ms (5.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (30.8%)

Profiling