Details

analyze1.0s (12%)

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)

sample74.0ms (0.9%)

Algorithm

1×

intervals

Results

41.0ms	112×	body	1024	valid
9.0ms	39×	body	512	valid
6.0ms	80×	body	128	valid
5.0ms	5×	body	2048	valid
3.0ms	20×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify168.0ms (1.9%)

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: 13.3b

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)))
3.0b	(cos.f64 (+.f64 a b))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_445`
19×	`*-un-lft-identity_binary64_423` `times-frac_binary64_429` `add-cube-cbrt_binary64_458`
13×	`associate-r_binary64_363`
10×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
5×	`pow1_binary64_484`
3×	`associate-l_binary64_364` `add-log-exp_binary64_462` `associate-/l_binary64_368` `associate-/r_binary64_367`
2×	`prod-exp_binary64_472` `div-inv_binary64_420` `unswap-sqr_binary64_391` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `cos-sum_binary64_557` `associate-r/_binary64_365` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434`

Counts

3 → 67

Calls

3 calls:

9.0ms	(*.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)))

series347.0ms (4%)

Counts

3 → 9

Calls

3 calls:

222.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
97.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
27.0ms	(cos.f64 (+.f64 a b))

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5764	1258

prune308.0ms (3.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	12	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	12	77

Merged error: 0.1b

Counts

77 → 12

Compiler

Compiled 5405 to 2865 computations (47% 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))
0.3b	(/.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_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 a) (sin.f64 b)))))
10.0ms	(/.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))

series953.0ms (11%)

Counts

4 → 12

Calls

4 calls:

469.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
267.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
145.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
71.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5442	2752

prune690.0ms (8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	111	13	124

Merged error: 0.0b

Counts

124 → 13

Compiler

Compiled 14408 to 6880 computations (52.2% 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))

rewrite41.0ms (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))
8.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series860.0ms (10%)

Counts

4 → 12

Calls

4 calls:

459.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
185.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
153.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
62.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4929	2353
1	4929	2353

prune215.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	109	10	119

Merged error: 0.0b

Counts

119 → 10

Compiler

Compiled 4512 to 1815 computations (59.8% 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 a) (sin.f64 b)))
0.1b	(*.f64 (sin.f64 b) r)
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite35.0ms (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 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
8.0ms	(-.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 (sin.f64 b) r)

series815.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

546.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
146.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
70.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
52.0ms	(*.f64 (sin.f64 b) r)

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5159	1643

prune82.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	89	9	98

Merged error: 0.0b

Counts

98 → 9

Compiler

Compiled 2138 to 514 computations (76% saved)

regimes67.0ms (0.8%)

Compiler: Compiled 627 to 405 computations (35.4% 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%)

sample2.5s (29%)

Algorithm

1×

intervals

Results

1.3s	3485×	body	1024	valid
327.0ms	1381×	body	512	valid
183.0ms	210×	body	2048	valid
172.0ms	2341×	body	128	valid
95.0ms	583×	body	256	valid

Compiler

Compiled 230 to 152 computations (33.9% saved)

Details

analyze1.0s (12%)

sample74.0ms (0.9%)

simplify168.0ms (1.9%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite24.0ms (0.3%)

series347.0ms (4%)

simplify89.0ms (1%)

prune308.0ms (3.6%)

localize15.0ms (0.2%)

rewrite46.0ms (0.5%)

series953.0ms (11%)

simplify82.0ms (1%)

prune690.0ms (8%)

localize14.0ms (0.2%)

rewrite41.0ms (0.5%)

series860.0ms (10%)

simplify82.0ms (1%)

prune215.0ms (2.5%)

localize15.0ms (0.2%)

rewrite35.0ms (0.4%)

series815.0ms (9.4%)

simplify58.0ms (0.7%)

prune82.0ms (0.9%)

regimes67.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.5s (29%)

Profiling