Details

analyze230.0ms (5.3%)

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)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify213.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5209	29

prune6.0ms (0.2%)

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 (0.3%)

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 (2.8%)

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:

52.0ms	(.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))

series248.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
80.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
48.0ms	(-.f64 (.f64 b b) (.f64 a a))
21.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify136.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4947	7997
1	4947	7997

prune707.0ms (16.4%)

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 15612 to 8950 computations (42.7% 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))

rewrite38.0ms (0.9%)

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:

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))

series154.0ms (3.6%)

Counts

2 → 6

Calls

2 calls:

89.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
64.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify67.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5176	2615

prune463.0ms (10.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	8	2	10
Picked	0	1	1
Done	0	0	0
Total	128	11	139

Merged error: 0.0b

Counts

139 → 11

Compiler

Compiled 9596 to 6401 computations (33.3% saved)

localize10.0ms (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 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
0.5b	(/.f64 1 (*.f64 b a))

rewrite60.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

215×	`add-exp-log_binary64_461`
115×	`prod-exp_binary64_472`
103×	`times-frac_binary64_429`
84×	`*-un-lft-identity_binary64_423`
77×	`div-exp_binary64_474`
67×	`add-cbrt-cube_binary64_459`
56×	`add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
37×	`1-exp_binary64_467`
26×	`cbrt-unprod_binary64_456`
22×	`cbrt-undiv_binary64_457`
16×	`rec-exp_binary64_473` `associate-/l*_binary64_368`
14×	`distribute-lft-out_binary64_374`
11×	`pow1_binary64_484`
8×	`div-inv_binary64_420`
7×	`associate-r_binary64_363`
5×	`associate-/r*_binary64_367`
4×	`pow-prod-down_binary64_494`
3×	`associate-*l/_binary64_366` `add-log-exp_binary64_462`
2×	`associate-/r/_binary64_369` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow-flip_binary64_497`
1×	`frac-times_binary64_433` `associate-l_binary64_364` `flip-+_binary64_397` `un-div-inv_binary64_421` `associate-r/_binary64_365` `associate-/l/_binary64_370` `-commutative_binary64_354` `flip3-+_binary64_426` `inv-pow_binary64_508`

Counts

3 → 197

Calls

3 calls:

20.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
5.0ms	(/.f64 1 (*.f64 b a))

series164.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

89.0ms	(.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (/.f64 1 (*.f64 b a)))
56.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))
19.0ms	(/.f64 1 (*.f64 b a))

simplify103.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4935	3715
1	4935	3715

prune250.0ms (5.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	5	4	9
Picked	0	1	1
Done	1	0	1
Total	209	8	217

Merged error: 0.0b

Counts

217 → 8

Compiler

Compiled 5097 to 2987 computations (41.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 b a)) (+.f64 b a))
0.5b	(/.f64 (/.f64 PI.f64 2) (*.f64 b a))

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

209×	`times-frac_binary64_429`
110×	`*-un-lft-identity_binary64_423`
74×	`add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
32×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
30×	`associate-/l*_binary64_368`
18×	`distribute-lft-out_binary64_374`
17×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
14×	`div-inv_binary64_420`
5×	`associate-/r*_binary64_367`
4×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
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` `flip3-+_binary64_426`

Counts

2 → 158

Calls

2 calls:

15.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 b a)) (+.f64 b a))
10.0ms	(/.f64 (/.f64 PI.f64 2) (*.f64 b a))

series118.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

79.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (*.f64 b a)) (+.f64 b a))
39.0ms	(/.f64 (/.f64 PI.f64 2) (*.f64 b a))

simplify104.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4992	3914
1	4992	3914

prune184.0ms (4.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	163	9	172

Merged error: 0b

Counts

172 → 9

Compiler

Compiled 3857 to 2078 computations (46.1% saved)

regimes36.0ms (0.8%)

Compiler: Compiled 266 to 220 computations (17.3% 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%)

sample804.0ms (18.6%)

Algorithm

1×

intervals

Results

479.0ms	8000×	body	128	valid
22.0ms	368×	body	128	invalid

Compiler

Compiled 164 to 135 computations (17.7% saved)

Details

analyze230.0ms (5.3%)

sample24.0ms (0.5%)

simplify213.0ms (4.9%)

prune6.0ms (0.2%)

localize12.0ms (0.3%)

rewrite123.0ms (2.8%)

series248.0ms (5.8%)

simplify136.0ms (3.1%)

prune707.0ms (16.4%)

localize9.0ms (0.2%)

rewrite38.0ms (0.9%)

series154.0ms (3.6%)

simplify67.0ms (1.5%)

prune463.0ms (10.7%)

localize10.0ms (0.2%)

rewrite60.0ms (1.4%)

series164.0ms (3.8%)

simplify103.0ms (2.4%)

prune250.0ms (5.8%)

localize7.0ms (0.2%)

rewrite42.0ms (1%)

series118.0ms (2.7%)

simplify104.0ms (2.4%)

prune184.0ms (4.3%)

regimes36.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample804.0ms (18.6%)

Profiling