Details

analyze1.0s (14.7%)

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample61.0ms (0.9%)

Algorithm

1×

intervals

Results

17.0ms	194×	body	128	valid
10.0ms	28×	body	1024	valid
7.0ms	74×	body	128	invalid
6.0ms	21×	body	512	valid
3.0ms	8×	body	1024	invalid
2.0ms	13×	body	256	valid
2.0ms	7×	body	512	invalid
2.0ms	9×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify337.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	4892	24
1	4892	24

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 30.8b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
3.7b	(.f64 (.f64 x (pow.f64 s 2)) x)
8.9b	(*.f64 x (pow.f64 s 2))
20.2b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-exp-log_binary64_461`
82×	`prod-exp_binary64_472`
34×	`add-cbrt-cube_binary64_459`
18×	`pow-to-exp_binary64_492` `pow-exp_binary64_491` `add-sqr-sqrt_binary64_445`
16×	`div-exp_binary64_474` `cbrt-unprod_binary64_456`
12×	`-un-lft-identity_binary64_423` `associate-l_binary64_364` `add-cube-cbrt_binary64_458` `associate-r*_binary64_363`
7×	`unpow-prod-down_binary64_502`
6×	`pow1_binary64_484`
4×	`add-log-exp_binary64_462` `unswap-sqr_binary64_391` `cbrt-undiv_binary64_457`
3×	`times-frac_binary64_429` `-commutative_binary64_354` `unpow2_binary64_488` `associate-/l_binary64_368` `sqr-pow_binary64_395`
1×	`cos-2_binary64_565` `pow-prod-down_binary64_494` `div-sub_binary64_428` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `associate-/r*_binary64_367`

Counts

4 → 119

Calls

4 calls:

15.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
11.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
7.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
7.0ms	(*.f64 x (pow.f64 s 2))

series332.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
104.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
51.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
47.0ms	(*.f64 x (pow.f64 s 2))

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4946	2214
1	4946	2214

prune367.0ms (5.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	12	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Merged error: 1.7b

Counts

132 → 12

Compiler

Compiled 6848 to 4202 computations (38.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
0.7b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
5.0b	(.f64 s (.f64 c x))
5.0b	(.f64 s (.f64 c x))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
14×	`add-sqr-sqrt_binary64_445`
12×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
9×	`associate-l_binary64_364`
8×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
7×	`pow-prod-down_binary64_494`
5×	`associate-r_binary64_363`
4×	`add-log-exp_binary64_462`
3×	`times-frac_binary64_429` `swap-sqr_binary64_390` `-commutative_binary64_354` `associate-/l_binary64_368`
2×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`cos-2_binary64_565` `pow-sqr_binary64_396` `sqr-abs_binary64_438` `pow-prod-up_binary64_493` `div-sub_binary64_428` `pow-plus_binary64_486` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `unswap-sqr_binary64_391` `associate-/r*_binary64_367` `pow2_binary64_504`

Counts

4 → 84

Calls

4 calls:

5.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
4.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

series338.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
51.0ms	(.f64 s (.f64 c x))
47.0ms	(.f64 s (.f64 c x))
41.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4976	1306
1	4976	1306

prune653.0ms (9.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	84	12	96
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	91	17	108

Merged error: 1.4b

Counts

108 → 17

Compiler

Compiled 12367 to 7931 computations (35.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(cos.f64 (*.f64 x 2))
0.5b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
5.0b	(.f64 s (.f64 c x))
5.0b	(.f64 s (.f64 c x))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
14×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445` `pow1_binary64_484`
9×	`times-frac_binary64_429`
6×	`pow-prod-down_binary64_494` `associate-l_binary64_364` `prod-exp_binary64_472` `cbrt-unprod_binary64_456`
4×	`add-log-exp_binary64_462`
3×	`associate-/l_binary64_368` `associate-/r_binary64_367`
2×	`-commutative_binary64_354` `associate-r*_binary64_363`
1×	`clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474`

Counts

4 → 70

Calls

4 calls:

8.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
4.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
2.0ms	(cos.f64 (*.f64 x 2))

series226.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
51.0ms	(.f64 s (.f64 c x))
50.0ms	(.f64 s (.f64 c x))
10.0ms	(cos.f64 (*.f64 x 2))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5369	1235

prune249.0ms (3.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	4	12	16
Picked	0	1	1
Done	0	0	0
Total	82	17	99

Merged error: 1.4b

Counts

99 → 17

Compiler

Compiled 5077 to 2836 computations (44.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(cos.f64 (*.f64 x 2))
0.4b	(/.f64 1 (/.f64 (fabs.f64 (.f64 s (.f64 c x))) (cos.f64 (*.f64 x 2))))
5.0b	(.f64 s (.f64 c x))
5.0b	(.f64 s (.f64 c x))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64_429`
48×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
25×	`add-exp-log_binary64_461`
19×	`add-cbrt-cube_binary64_459`
15×	`pow1_binary64_484`
13×	`associate-/r*_binary64_367`
7×	`div-exp_binary64_474`
6×	`pow-prod-down_binary64_494` `associate-l_binary64_364` `prod-exp_binary64_472` `cbrt-unprod_binary64_456`
5×	`div-inv_binary64_420`
4×	`add-log-exp_binary64_462`
3×	`associate-/l*_binary64_368` `cbrt-undiv_binary64_457`
2×	`rec-exp_binary64_473` `1-exp_binary64_467` `-commutative_binary64_354` `associate-r*_binary64_363`
1×	`associate-/r/_binary64_369` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow-flip_binary64_497` `inv-pow_binary64_508`

Counts

4 → 119

Calls

4 calls:

9.0ms	(/.f64 1 (/.f64 (fabs.f64 (.f64 s (.f64 c x))) (cos.f64 (*.f64 x 2))))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
2.0ms	(cos.f64 (*.f64 x 2))

series227.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(/.f64 1 (/.f64 (fabs.f64 (.f64 s (.f64 c x))) (cos.f64 (*.f64 x 2))))
49.0ms	(.f64 s (.f64 c x))
45.0ms	(.f64 s (.f64 c x))
10.0ms	(cos.f64 (*.f64 x 2))

simplify117.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4909	2922
1	4909	2922

prune183.0ms (2.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	15	15
Picked	1	0	1
Done	0	1	1
Total	131	17	148

Merged error: 1.4b

Counts

148 → 17

Compiler

Compiled 4422 to 1999 computations (54.8% saved)

regimes143.0ms (2.1%)

Compiler: Compiled 1588 to 1096 computations (31% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	28
1	15	28

end0.0ms (0%)

sample2.3s (32.9%)

Algorithm

1×

intervals

Results

550.0ms	6120×	body	128	valid
362.0ms	926×	body	1024	valid
311.0ms	1894×	body	128	invalid
173.0ms	618×	body	512	valid
81.0ms	222×	body	1024	invalid
63.0ms	332×	body	256	valid
52.0ms	208×	body	512	invalid
28.0ms	146×	body	256	invalid
3.0ms	4×	body	2048	valid

Compiler

Compiled 429 to 296 computations (31% saved)

Details

analyze1.0s (14.7%)

sample61.0ms (0.9%)

simplify337.0ms (4.8%)

prune3.0ms (0%)

localize13.0ms (0.2%)

rewrite52.0ms (0.7%)

series332.0ms (4.8%)

simplify85.0ms (1.2%)

prune367.0ms (5.3%)

localize10.0ms (0.2%)

rewrite28.0ms (0.4%)

series338.0ms (4.9%)

simplify63.0ms (0.9%)

prune653.0ms (9.4%)

localize10.0ms (0.2%)

rewrite25.0ms (0.4%)

series226.0ms (3.2%)

simplify75.0ms (1.1%)

prune249.0ms (3.6%)

localize12.0ms (0.2%)

rewrite35.0ms (0.5%)

series227.0ms (3.3%)

simplify117.0ms (1.7%)

prune183.0ms (2.6%)

regimes143.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (32.9%)

Profiling