Details

analyze1.0s (10.8%)

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
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample73.0ms (0.8%)

Algorithm

1×

intervals

Results

37.0ms	99×	body	1024	valid
12.0ms	55×	body	512	valid
6.0ms	8×	body	2048	valid
5.0ms	74×	body	128	valid
3.0ms	20×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify165.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune2.0ms (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: 15.4b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
2.1b	(cos.f64 (+.f64 a b))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_435`
19×	`times-frac_binary64_420` `add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
13×	`associate-r_binary64_356`
10×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
5×	`pow1_binary64_472`
3×	`associate-l_binary64_357` `add-log-exp_binary64_450` `associate-/l_binary64_361` `associate-/r_binary64_360`
2×	`div-inv_binary64_411` `cbrt-undiv_binary64_445` `prod-exp_binary64_460` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `-commutative_binary64_347` `cos-sum_binary64_545` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `associate-r/_binary64_358`

Counts

3 → 67

Calls

3 calls:

8.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
5.0ms	(cos.f64 (+.f64 a b))
5.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))

series343.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

220.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
96.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
27.0ms	(cos.f64 (+.f64 a b))

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4887	1258
1	4887	1258

prune72.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	9	77

Merged error: 0.2b

Counts

77 → 9

Compiler

Compiled 1305 to 318 computations (75.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_435`
22×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
20×	`associate-r_binary64_356`
19×	`times-frac_binary64_420`
13×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`associate-/r/_binary64_362` `pow1_binary64_472`
7×	`sin-mult_binary64_566`
6×	`cos-mult_binary64_565` `associate-l_binary64_357` `add-log-exp_binary64_450`
3×	`flip3--_binary64_418` `frac-sub_binary64_423` `prod-exp_binary64_460` `flip--_binary64_389` `unswap-sqr_binary64_382` `associate-/l_binary64_361` `cbrt-unprod_binary64_444` `sub-div_binary64_421` `associate-/r_binary64_360`
2×	`div-inv_binary64_411` `*-commutative_binary64_347` `cbrt-undiv_binary64_445` `pow-prod-down_binary64_482` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `sub-neg_binary64_407` `frac-2neg_binary64_425` `associate-*r/_binary64_358`

Counts

4 → 99

Calls

4 calls:

16.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series969.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

486.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
271.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
141.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
71.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4915	2742
1	4915	2742

prune129.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	108	12	120

Merged error: 0b

Counts

120 → 12

Compiler

Compiled 2983 to 594 computations (80.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.1b	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
0.2b	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
0.2b	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_435`
28×	`*-un-lft-identity_binary64_414`
18×	`times-frac_binary64_420` `add-cube-cbrt_binary64_446`
13×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`associate-/r*_binary64_360`
6×	`pow1_binary64_472` `add-log-exp_binary64_450`
5×	`distribute-lft-out--_binary64_368` `difference-of-squares_binary64_383`
4×	`associate-/l*_binary64_361`
3×	`cbrt-undiv_binary64_445` `associate-l_binary64_357` `associate-r_binary64_356` `div-exp_binary64_462`
2×	`associate-/r/_binary64_362` `flip3--_binary64_418` `clear-num_binary64_413` `cos-mult_binary64_565` `div-inv_binary64_411` `prod-exp_binary64_460` `frac-2neg_binary64_425` `flip--_binary64_389` `cbrt-unprod_binary64_444`
1×	`diff-log_binary64_503` `*-commutative_binary64_347` `pow-prod-down_binary64_482` `sub-neg_binary64_407` `unswap-sqr_binary64_382` `associate-/l/_binary64_363`

Counts

4 → 91

Calls

4 calls:

9.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
8.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
6.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series821.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

432.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
173.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
144.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
72.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify104.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4917	2329
1	4917	2329

prune99.0ms (1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	105	10	115

Merged error: 0b

Counts

115 → 10

Compiler

Compiled 2320 to 508 computations (78.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(*.f64 (sin.f64 b) r)
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_435`
13×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
10×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
8×	`pow1_binary64_472`
6×	`associate-l_binary64_357` `add-log-exp_binary64_450` `associate-r_binary64_356`
5×	`sin-mult_binary64_566`
4×	`associate-/r/_binary64_362` `cos-mult_binary64_565`
3×	`times-frac_binary64_420` `prod-exp_binary64_460` `cbrt-unprod_binary64_444` `associate-/r*_binary64_360`
2×	`flip3--_binary64_418` `*-commutative_binary64_347` `frac-sub_binary64_423` `cbrt-undiv_binary64_445` `pow-prod-down_binary64_482` `flip--_binary64_389` `unswap-sqr_binary64_382` `sub-div_binary64_421` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `div-inv_binary64_411` `sub-neg_binary64_407` `frac-2neg_binary64_425` `associate-/l*_binary64_361`

Counts

4 → 75

Calls

4 calls:

12.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
4.0ms	(*.f64 (sin.f64 b) r)

series813.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

533.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
153.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
70.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
56.0ms	(*.f64 (sin.f64 b) r)

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4967	1633
1	4967	1633

prune70.0ms (0.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	87	10	97

Merged error: 0b

Counts

97 → 10

Compiler

Compiled 1880 to 361 computations (80.8% saved)

regimes742.0ms (7.8%)

Compiler: Compiled 8783 to 5269 computations (40% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	21
1	23	21

end0.0ms (0%)

sample3.7s (38.6%)

Algorithm

1×

intervals

Results

1.3s	3508×	body	1024	valid
304.0ms	1383×	body	512	valid
182.0ms	2312×	body	128	valid
173.0ms	200×	body	2048	valid
90.0ms	597×	body	256	valid

Compiler

Compiled 1736 to 1044 computations (39.9% saved)

Details

analyze1.0s (10.8%)

sample73.0ms (0.8%)

simplify165.0ms (1.7%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite23.0ms (0.2%)

series343.0ms (3.6%)

simplify71.0ms (0.7%)

prune72.0ms (0.8%)

localize15.0ms (0.2%)

rewrite46.0ms (0.5%)

series969.0ms (10.2%)

simplify77.0ms (0.8%)

prune129.0ms (1.4%)

localize16.0ms (0.2%)

rewrite36.0ms (0.4%)

series821.0ms (8.7%)

simplify104.0ms (1.1%)

prune99.0ms (1%)

localize15.0ms (0.2%)

rewrite33.0ms (0.4%)

series813.0ms (8.6%)

simplify56.0ms (0.6%)

prune70.0ms (0.7%)

regimes742.0ms (7.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.7s (38.6%)

Profiling