Details

analyze1.0s (12.4%)

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 (0.9%)

Algorithm

1×

intervals

Results

36.0ms	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)

simplify174.0ms (2.1%)

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: 15.4b

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 (sin.f64 b))
0.3b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
2.1b	(cos.f64 (+.f64 a b))

rewrite19.0ms (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))

series307.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

216.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
59.0ms	(*.f64 r (sin.f64 b))
31.0ms	(cos.f64 (+.f64 a b))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4847	692
1	4847	692

prune163.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 0.2b

Counts

57 → 7

Compiler

Compiled 2391 to 1433 computations (40.1% 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 r (sin.f64 b))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite32.0ms (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:

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))

series800.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

504.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
157.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
80.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
58.0ms	(*.f64 r (sin.f64 b))

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	6468	1592

prune389.0ms (4.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 0b

Counts

95 → 9

Compiler

Compiled 7794 to 3603 computations (53.8% saved)

localize14.0ms (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))

rewrite38.0ms (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:

10.0ms	(/.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))

series848.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

447.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
179.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
159.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
62.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify84.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4929	2353
1	4929	2353

prune280.0ms (3.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	105	10	115

Merged error: 0b

Counts

115 → 10

Compiler

Compiled 6162 to 2529 computations (59% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

9.0ms	(/.f64 r (-.f64 (*.f64 (cos.f64 a) (/.f64 (cos.f64 b) (sin.f64 b))) (sin.f64 a)))
8.0ms	(*.f64 (cos.f64 a) (/.f64 (cos.f64 b) (sin.f64 b)))
7.0ms	(-.f64 (*.f64 (cos.f64 a) (/.f64 (cos.f64 b) (sin.f64 b))) (sin.f64 a))
4.0ms	(/.f64 (cos.f64 b) (sin.f64 b))

series810.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

450.0ms	(/.f64 r (-.f64 (*.f64 (cos.f64 a) (/.f64 (cos.f64 b) (sin.f64 b))) (sin.f64 a)))
171.0ms	(-.f64 (*.f64 (cos.f64 a) (/.f64 (cos.f64 b) (sin.f64 b))) (sin.f64 a))
143.0ms	(*.f64 (cos.f64 a) (/.f64 (cos.f64 b) (sin.f64 b)))
47.0ms	(/.f64 (cos.f64 b) (sin.f64 b))

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4973	2399
1	4973	2399

prune145.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	114	10	124

Merged error: 0b

Counts

124 → 10

Compiler

Compiled 3415 to 1060 computations (69% saved)

regimes75.0ms (0.9%)

Compiler: Compiled 735 to 450 computations (38.8% 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%)

sample2.7s (32.5%)

Algorithm

1×

intervals

Results

1.5s	3508×	body	1024	valid
322.0ms	1383×	body	512	valid
173.0ms	200×	body	2048	valid
162.0ms	2312×	body	128	valid
91.0ms	597×	body	256	valid

Compiler

Compiled 266 to 167 computations (37.2% saved)

Details

analyze1.0s (12.4%)

sample73.0ms (0.9%)

simplify174.0ms (2.1%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite19.0ms (0.2%)

series307.0ms (3.7%)

simplify83.0ms (1%)

prune163.0ms (2%)

localize15.0ms (0.2%)

rewrite32.0ms (0.4%)

series800.0ms (9.6%)

simplify78.0ms (0.9%)

prune389.0ms (4.7%)

localize14.0ms (0.2%)

rewrite38.0ms (0.5%)

series848.0ms (10.2%)

simplify84.0ms (1%)

prune280.0ms (3.4%)

localize14.0ms (0.2%)

rewrite39.0ms (0.5%)

series810.0ms (9.8%)

simplify78.0ms (0.9%)

prune145.0ms (1.7%)

regimes75.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (32.5%)

Profiling