Details

analyze1.0s (10.5%)

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)

sample78.0ms (0.8%)

Algorithm

1×

intervals

Results

43.0ms	103×	body	1024	valid
11.0ms	50×	body	512	valid
6.0ms	79×	body	128	valid
5.0ms	6×	body	2048	valid
3.0ms	18×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify166.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

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: 14.8b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
3.8b	(cos.f64 (+.f64 a b))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
9×	`add-sqr-sqrt_binary64_445`
7×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
5×	`pow1_binary64_484`
3×	`times-frac_binary64_429` `associate-l_binary64_364` `associate-r_binary64_363` `add-log-exp_binary64_462` `associate-/r*_binary64_367`
2×	`prod-exp_binary64_472` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `cos-sum_binary64_557` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `unswap-sqr_binary64_391` `associate-/l_binary64_368`

Counts

3 → 47

Calls

3 calls:

5.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0ms	(*.f64 r (sin.f64 b))
4.0ms	(cos.f64 (+.f64 a b))

series301.0ms (3%)

Counts

3 → 9

Calls

3 calls:

219.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
56.0ms	(*.f64 r (sin.f64 b))
26.0ms	(cos.f64 (+.f64 a b))

simplify82.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4847	692
1	4847	692

prune210.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	11	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	11	57

Merged error: 0.2b

Counts

57 → 11

Compiler

Compiled 3241 to 1839 computations (43.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_445`
13×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
10×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
8×	`pow1_binary64_484`
6×	`associate-l_binary64_364` `associate-r_binary64_363` `add-log-exp_binary64_462`
5×	`sin-mult_binary64_578`
4×	`cos-mult_binary64_577` `associate-/r/_binary64_369`
3×	`times-frac_binary64_429` `prod-exp_binary64_472` `associate-/r*_binary64_367` `cbrt-unprod_binary64_456`
2×	`pow-prod-down_binary64_494` `flip3--_binary64_427` `*-commutative_binary64_354` `flip--_binary64_398` `unswap-sqr_binary64_391` `sub-div_binary64_430` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `frac-sub_binary64_432`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `associate-/l*_binary64_368`

Counts

4 → 76

Calls

4 calls:

10.0ms	(/.f64 (.f64 r (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))
5.0ms	(*.f64 r (sin.f64 b))

series785.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

508.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.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)))
68.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
55.0ms	(*.f64 r (sin.f64 b))

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	6468	1592

prune394.0ms (4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	87	12	99

Merged error: 0.0b

Counts

99 → 12

Compiler

Compiled 7616 to 3615 computations (52.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_445`
29×	`*-un-lft-identity_binary64_423`
19×	`add-cube-cbrt_binary64_458`
18×	`times-frac_binary64_429`
13×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`associate-/r*_binary64_367`
6×	`pow1_binary64_484` `add-log-exp_binary64_462`
5×	`distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392`
4×	`associate-/l*_binary64_368`
3×	`associate-l_binary64_364` `cancel-sign-sub-inv_binary64_389` `associate-r_binary64_363` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
2×	`prod-exp_binary64_472` `flip3--_binary64_427` `cos-mult_binary64_577` `associate-/r/_binary64_369` `clear-num_binary64_422` `frac-2neg_binary64_434` `flip--_binary64_398` `div-inv_binary64_420` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `sub-neg_binary64_416` `diff-log_binary64_515` `associate-/l/_binary64_370` `*-commutative_binary64_354` `unswap-sqr_binary64_391`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
9.0ms	(-.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))

series846.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

448.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
178.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
158.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
62.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4929	2353
1	4929	2353

prune351.0ms (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 0.0b

Counts

118 → 11

Compiler

Compiled 7164 to 3303 computations (53.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite74.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`times-frac_binary64_429`
112×	`add-sqr-sqrt_binary64_445`
77×	`*-un-lft-identity_binary64_423`
67×	`add-cube-cbrt_binary64_458`
23×	`associate-/r*_binary64_367`
15×	`difference-of-squares_binary64_392`
13×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
9×	`associate-/l*_binary64_368`
7×	`div-inv_binary64_420`
6×	`add-log-exp_binary64_462`
5×	`distribute-lft-out--_binary64_375` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
4×	`pow1_binary64_484`
3×	`cancel-sign-sub-inv_binary64_389` `associate-/r/_binary64_369` `clear-num_binary64_422` `frac-2neg_binary64_434`
2×	`flip3--_binary64_427` `flip--_binary64_398`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `quot-tan_binary64_583`

Counts

4 → 161

Calls

4 calls:

23.0ms	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (sin.f64 a)))
22.0ms	(-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (sin.f64 a))
7.0ms	(/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b)))
4.0ms	(/.f64 (sin.f64 b) (cos.f64 b))

series812.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

446.0ms	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (sin.f64 a)))
181.0ms	(-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (sin.f64 a))
140.0ms	(/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b)))
46.0ms	(/.f64 (sin.f64 b) (cos.f64 b))

simplify118.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4930	4552
1	4930	4552

prune200.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	174	10	184

Merged error: 0b

Counts

184 → 10

Compiler

Compiled 5218 to 1407 computations (73% saved)

regimes612.0ms (6.2%)

Compiler: Compiled 4812 to 3030 computations (37% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms (0%)

sample3.5s (35.6%)

Algorithm

1×

intervals

Results

1.4s	3599×	body	1024	valid
322.0ms	1397×	body	512	valid
181.0ms	200×	body	2048	valid
176.0ms	2232×	body	128	valid
92.0ms	572×	body	256	valid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 1217 to 770 computations (36.7% saved)

Details

analyze1.0s (10.5%)

sample78.0ms (0.8%)

simplify166.0ms (1.7%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite17.0ms (0.2%)

series301.0ms (3%)

simplify82.0ms (0.8%)

prune210.0ms (2.1%)

localize16.0ms (0.2%)

rewrite32.0ms (0.3%)

series785.0ms (7.9%)

simplify78.0ms (0.8%)

prune394.0ms (4%)

localize15.0ms (0.1%)

rewrite38.0ms (0.4%)

series846.0ms (8.5%)

simplify83.0ms (0.8%)

prune351.0ms (3.5%)

localize14.0ms (0.1%)

rewrite74.0ms (0.7%)

series812.0ms (8.2%)

simplify118.0ms (1.2%)

prune200.0ms (2%)

regimes612.0ms (6.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.5s (35.6%)

Profiling