Details

analyze236.0ms (4%)

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	20×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify208.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5209	29

prune6.0ms (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: 17.4b

Counts

2 → 2

Compiler

Compiled 99 to 79 computations (20.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.8b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
5.7b	(-.f64 (.f64 b b) (.f64 a a))
10.1b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite123.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64_429`
178×	`add-sqr-sqrt_binary64_445`
153×	`*-un-lft-identity_binary64_423`
121×	`add-cube-cbrt_binary64_458`
58×	`associate-l_binary64_364`
46×	`difference-of-squares_binary64_392`
40×	`cancel-sign-sub-inv_binary64_389`
22×	`div-inv_binary64_420`
19×	`associate-r_binary64_363`
18×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
14×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `distribute-lft-out--_binary64_375`
13×	`associate-/l*_binary64_368`
8×	`add-log-exp_binary64_462`
6×	`pow1_binary64_484` `flip3--_binary64_427` `flip--_binary64_398` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
4×	`sub-neg_binary64_416` `associate-/r/_binary64_369` `associate-/r*_binary64_367`
3×	`frac-times_binary64_433` `prod-exp_binary64_472` `associate-*r/_binary64_365` `unswap-sqr_binary64_391` `frac-sub_binary64_432` `cbrt-unprod_binary64_456`
2×	`diff-log_binary64_515`
1×	`pow-prod-down_binary64_494` `associate-/l/_binary64_370` `associate-l/_binary64_366` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434`

Counts

4 → 270

Calls

4 calls:

53.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
17.0ms	(-.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))

series230.0ms (3.9%)

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)))
65.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
43.0ms	(-.f64 (.f64 b b) (.f64 a a))
21.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify139.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4947	7997
1	4947	7997

prune694.0ms (11.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	271	11	282
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	273	11	284

Merged error: 0.1b

Counts

284 → 11

Compiler

Compiled 15583 to 8925 computations (42.7% 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))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64_429`
79×	`*-un-lft-identity_binary64_423`
60×	`add-exp-log_binary64_461`
51×	`add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
39×	`add-cbrt-cube_binary64_459`
29×	`div-exp_binary64_474`
19×	`prod-exp_binary64_472`
17×	`cbrt-undiv_binary64_457`
14×	`distribute-lft-out_binary64_374` `associate-/l*_binary64_368`
10×	`cbrt-unprod_binary64_456`
7×	`div-inv_binary64_420`
6×	`1-exp_binary64_467`
5×	`associate-/r*_binary64_367`
2×	`pow1_binary64_484` `associate-/l/_binary64_370` `associate-/r/_binary64_369` `clear-num_binary64_422` `frac-2neg_binary64_434` `add-log-exp_binary64_462`
1×	`flip-+_binary64_397` `associate-*l/_binary64_366` `flip3-+_binary64_426`

Counts

2 → 122

Calls

2 calls:

17.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
10.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series167.0ms (2.8%)

Counts

2 → 6

Calls

2 calls:

100.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
67.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5176	2615

prune474.0ms (8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	8	2	10
Picked	0	1	1
Done	0	0	0
Total	127	12	139

Merged error: 0.0b

Counts

139 → 12

Compiler

Compiled 9618 to 6419 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite57.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

331×	`times-frac_binary64_429`
215×	`*-un-lft-identity_binary64_423`
135×	`add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
71×	`associate-/l*_binary64_368`
40×	`distribute-lft-out_binary64_374`
28×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
17×	`div-inv_binary64_420`
15×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
6×	`associate-/r/_binary64_369`
5×	`associate-/r*_binary64_367`
3×	`flip-+_binary64_397` `prod-exp_binary64_472` `flip3-+_binary64_426` `cbrt-unprod_binary64_456`
2×	`pow1_binary64_484` `associate-/l/_binary64_370` `clear-num_binary64_422` `frac-2neg_binary64_434` `add-log-exp_binary64_462`

Counts

2 → 226

Calls

2 calls:

20.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (*.f64 b a))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series149.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

82.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (*.f64 b a))
68.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify107.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4972	5513
1	4972	5513

prune368.0ms (6.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	227	5	232
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	232	12	244

Merged error: 0.0b

Counts

244 → 12

Compiler

Compiled 7289 to 4168 computations (42.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
0.3b	(.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (/.f64 1 (.f64 b a)))
0.5b	(/.f64 1 (*.f64 b a))

rewrite73.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

194×	`times-frac_binary64_429`
152×	`*-un-lft-identity_binary64_423`
107×	`add-sqr-sqrt_binary64_445`
98×	`add-cube-cbrt_binary64_458`
97×	`add-exp-log_binary64_461`
58×	`associate-l_binary64_364`
49×	`add-cbrt-cube_binary64_459`
40×	`div-exp_binary64_474`
33×	`prod-exp_binary64_472`
27×	`distribute-lft-out_binary64_374`
20×	`cbrt-undiv_binary64_457`
16×	`associate-/l*_binary64_368`
13×	`div-inv_binary64_420` `cbrt-unprod_binary64_456`
8×	`rec-exp_binary64_473` `1-exp_binary64_467` `pow1_binary64_484`
7×	`associate-r_binary64_363`
5×	`associate-/r*_binary64_367`
4×	`associate-/r/_binary64_369`
3×	`add-log-exp_binary64_462` `unswap-sqr_binary64_391`
2×	`pow-prod-down_binary64_494` `flip-+_binary64_397` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434` `pow-flip_binary64_497`
1×	`frac-times_binary64_433` `un-div-inv_binary64_421` `associate-r/_binary64_365` `associate-/l/_binary64_370` `associate-l/_binary64_366` `*-commutative_binary64_354` `inv-pow_binary64_508`

Counts

3 → 225

Calls

3 calls:

31.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (/.f64 1 (.f64 b a)))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
5.0ms	(/.f64 1 (*.f64 b a))

series164.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

83.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (/.f64 1 (.f64 b a)))
61.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
19.0ms	(/.f64 1 (*.f64 b a))

simplify112.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4956	4384
1	4956	4384

prune248.0ms (4.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	232	2	234
Fresh	4	5	9
Picked	0	1	1
Done	2	0	2
Total	238	8	246

Merged error: 0.0b

Counts

246 → 8

Compiler

Compiled 5285 to 2708 computations (48.8% saved)

regimes392.0ms (6.7%)

Compiler: Compiled 4862 to 3492 computations (28.2% 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%)

sample1.8s (30.1%)

Algorithm

1×

intervals

Results

460.0ms	8000×	body	128	valid
21.0ms	368×	body	128	invalid

Compiler

Compiled 1617 to 1161 computations (28.2% saved)

Details

analyze236.0ms (4%)

sample23.0ms (0.4%)

simplify208.0ms (3.5%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite123.0ms (2.1%)

series230.0ms (3.9%)

simplify139.0ms (2.4%)

prune694.0ms (11.8%)

localize8.0ms (0.1%)

rewrite41.0ms (0.7%)

series167.0ms (2.8%)

simplify63.0ms (1.1%)

prune474.0ms (8%)

localize7.0ms (0.1%)

rewrite57.0ms (1%)

series149.0ms (2.5%)

simplify107.0ms (1.8%)

prune368.0ms (6.3%)

localize9.0ms (0.2%)

rewrite73.0ms (1.2%)

series164.0ms (2.8%)

simplify112.0ms (1.9%)

prune248.0ms (4.2%)

regimes392.0ms (6.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (30.1%)

Profiling