Details

analyze1.0s (11.8%)

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)

sample78.0ms (0.9%)

Algorithm

1×

intervals

Results

44.0ms	111×	body	1024	valid
8.0ms	39×	body	512	valid
8.0ms	9×	body	2048	valid
5.0ms	78×	body	128	valid
3.0ms	19×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify173.0ms (2%)

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: 15.7b

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))
0.3b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.1b	(cos.f64 (+.f64 a b))

rewrite18.0ms (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:

6.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
5.0ms	(cos.f64 (+.f64 a b))
5.0ms	(*.f64 r (sin.f64 b))

series315.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

230.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
57.0ms	(*.f64 r (sin.f64 b))
27.0ms	(cos.f64 (+.f64 a b))

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4847	692
1	4847	692

prune173.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Merged error: 0.2b

Counts

57 → 8

Compiler

Compiled 2794 to 1498 computations (46.4% saved)

localize17.0ms (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)))
0.1b	(*.f64 r (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))))

rewrite34.0ms (0.4%)

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:

11.0ms	(/.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))

series796.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

505.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
152.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
81.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
58.0ms	(*.f64 r (sin.f64 b))

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	6468	1592

prune374.0ms (4.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 0.0b

Counts

96 → 12

Compiler

Compiled 7845 to 3466 computations (55.8% 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 b) (sin.f64 a)))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_445`
22×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
20×	`associate-r_binary64_363`
19×	`times-frac_binary64_429`
13×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`pow1_binary64_484` `associate-/r/_binary64_369`
7×	`sin-mult_binary64_578`
6×	`associate-l_binary64_364` `cos-mult_binary64_577` `add-log-exp_binary64_462`
3×	`prod-exp_binary64_472` `flip3--_binary64_427` `flip--_binary64_398` `unswap-sqr_binary64_391` `sub-div_binary64_430` `associate-/l_binary64_368` `associate-/r_binary64_367` `frac-sub_binary64_432` `cbrt-unprod_binary64_456`
2×	`pow-prod-down_binary64_494` `*-commutative_binary64_354` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `associate-*r/_binary64_365` `clear-num_binary64_422` `frac-2neg_binary64_434`

Counts

4 → 100

Calls

4 calls:

14.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
6.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

series989.0ms (11.5%)

Counts

4 → 12

Calls

4 calls:

501.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
279.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
141.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
68.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	6111	2856

prune267.0ms (3.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	113	11	124

Merged error: 0.0b

Counts

124 → 11

Compiler

Compiled 6502 to 2354 computations (63.8% 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))

rewrite39.0ms (0.5%)

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))

series847.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

461.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
177.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
142.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
67.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4929	2353
1	4929	2353

prune319.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	107	10	117

Merged error: 0.0b

Counts

117 → 10

Compiler

Compiled 6842 to 2925 computations (57.2% saved)

regimes79.0ms (0.9%)

Compiler: Compiled 861 to 465 computations (46% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms (0%)

sample2.7s (31%)

Algorithm

1×

intervals

Results

1.4s	3471×	body	1024	valid
315.0ms	1365×	body	512	valid
195.0ms	224×	body	2048	valid
163.0ms	2354×	body	128	valid
88.0ms	586×	body	256	valid
1.0ms	2×	body	512	invalid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 311 to 173 computations (44.4% saved)

Details

analyze1.0s (11.8%)

sample78.0ms (0.9%)

simplify173.0ms (2%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite18.0ms (0.2%)

series315.0ms (3.6%)

simplify81.0ms (0.9%)

prune173.0ms (2%)

localize17.0ms (0.2%)

rewrite34.0ms (0.4%)

series796.0ms (9.2%)

simplify75.0ms (0.9%)

prune374.0ms (4.3%)

localize15.0ms (0.2%)

rewrite46.0ms (0.5%)

series989.0ms (11.5%)

simplify88.0ms (1%)

prune267.0ms (3.1%)

localize16.0ms (0.2%)

rewrite39.0ms (0.5%)

series847.0ms (9.8%)

simplify83.0ms (1%)

prune319.0ms (3.7%)

regimes79.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (31%)

Profiling