Details

analyze893.0ms (11.9%)

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
18.7%	81.2%	0.1%	7
18.7%	81.2%	0.1%	8
29.7%	69.5%	0.9%	9
30.4%	67.9%	1.7%	10
36.3%	61.1%	2.6%	11
36.9%	59.5%	3.6%	12
39.9%	55.9%	4.2%	13
40.2%	54.9%	4.9%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample144.0ms (1.9%)

Algorithm

1×

intervals

Results

74.0ms	37×	body	2048	valid
26.0ms	54×	body	1024	valid
17.0ms	2×	body	4096	valid
7.0ms	27×	body	512	valid
7.0ms	122×	body	128	valid
2.0ms	14×	body	256	valid
1.0ms	1×	body	2048	invalid
0.0ms	5×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify181.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	287	20
1	287	20

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 19.0b

Counts

2 → 2

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
3.3b	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
32.8b	(tan.f64 (*.f64 PI.f64 l))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `tan-quot_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 66

Calls

4 calls:

7.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
4.0ms	(*.f64 PI.f64 l)
3.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series286.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(/.f64 (tan.f64 (.f64 PI.f64 l)) (.f64 F F))
81.0ms	(tan.f64 (*.f64 PI.f64 l))
29.0ms	(*.f64 PI.f64 l)
25.0ms	(*.f64 PI.f64 l)

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4967	914
1	4967	914

prune99.0ms (1.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	61	17	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	62	18	80

Merged error: 15.4b

Counts

80 → 18

Compiler

Compiled 1596 to 455 computations (71.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 PI.f64 l)
0.2b	(*.f64 PI.f64 l)
0.5b	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
32.8b	(tan.f64 (*.f64 PI.f64 l))

rewrite61.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

396×	`times-frac_binary64`
197×	`add-sqr-sqrt_binary64`
193×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
44×	`associate-/r*_binary64`
23×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64` `div-inv_binary64`
9×	`pow1_binary64` `div-exp_binary64`
6×	`associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64`
5×	`associate-/r/_binary64`
4×	`add-log-exp_binary64`
3×	`rec-exp_binary64` `associate-/l*_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `tan-quot_binary64`

Counts

4 → 245

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
4.0ms	(*.f64 PI.f64 l)
3.0ms	(*.f64 PI.f64 l)
2.0ms	(tan.f64 (*.f64 PI.f64 l))

series300.0ms (4%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
62.0ms	(tan.f64 (*.f64 PI.f64 l))
32.0ms	(*.f64 PI.f64 l)
25.0ms	(*.f64 PI.f64 l)

simplify124.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5075	6480

prune243.0ms (3.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	253	4	257
Fresh	3	14	17
Picked	0	1	1
Done	0	0	0
Total	256	19	275

Merged error: 15.4b

Counts

275 → 19

Compiler

Compiled 6336 to 1562 computations (75.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.0b	(cbrt.f64 PI.f64)
1.0b	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
33.1b	(tan.f64 (.f64 (.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)) (*.f64 l (cbrt.f64 PI.f64))))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
8×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 70

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
3.0ms	(tan.f64 (.f64 (.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)) (*.f64 l (cbrt.f64 PI.f64))))
1.0ms	(cbrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)

series65.0ms (0.9%)

Counts

4 → 6

Calls

4 calls:

65.0ms	(tan.f64 (.f64 (.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)) (*.f64 l (cbrt.f64 PI.f64))))
0.0ms	(*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)

simplify60.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5232	747

prune97.0ms (1.3%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	3	14	17
Picked	0	1	1
Done	0	1	1
Total	77	18	95

Merged error: 15.4b

Counts

95 → 18

Compiler

Compiled 2059 to 852 computations (58.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 PI.f64)
1.0b	(cbrt.f64 PI.f64)
1.0b	(*.f64 (sqrt.f64 (cbrt.f64 PI.f64)) (pow.f64 (sqrt.f64 (cbrt.f64 PI.f64)) 3))
32.9b	(tan.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 PI.f64)) (pow.f64 (sqrt.f64 (cbrt.f64 PI.f64)) 3)) (*.f64 l (cbrt.f64 PI.f64))))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64`
46×	`sqrt-prod_binary64`
29×	`cbrt-prod_binary64`
24×	`associate-r_binary64` `unswap-sqr_binary64`
18×	`unpow-prod-down_binary64` `cube-prod_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`add-exp-log_binary64` `associate-l_binary64`
6×	`add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`prod-exp_binary64`
2×	`pow1/3_binary64`
1×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-exp_binary64` `unpow3_binary64` `tan-quot_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 100

Calls

4 calls:

15.0ms	(*.f64 (sqrt.f64 (cbrt.f64 PI.f64)) (pow.f64 (sqrt.f64 (cbrt.f64 PI.f64)) 3))
4.0ms	(tan.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 PI.f64)) (pow.f64 (sqrt.f64 (cbrt.f64 PI.f64)) 3)) (*.f64 l (cbrt.f64 PI.f64))))
1.0ms	(cbrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)

series70.0ms (0.9%)

Counts

4 → 6

Calls

4 calls:

70.0ms	(tan.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 PI.f64)) (pow.f64 (sqrt.f64 (cbrt.f64 PI.f64)) 3)) (*.f64 l (cbrt.f64 PI.f64))))
0.0ms	(*.f64 (sqrt.f64 (cbrt.f64 PI.f64)) (pow.f64 (sqrt.f64 (cbrt.f64 PI.f64)) 3))
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4886	1537
1	4886	1537

prune119.0ms (1.6%)

Pruning

20 alts after pruning (17 fresh and 3 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	1	14	15
Picked	0	1	1
Done	0	2	2
Total	104	20	124

Merged error: 15.4b

Counts

124 → 20

Compiler

Compiled 2917 to 1174 computations (59.8% saved)

regimes249.0ms (3.3%)

Compiler: Compiled 2723 to 1762 computations (35.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	23
1	33	23

end0.0ms (0%)

sample4.2s (56.4%)

Algorithm

1×

intervals

Results

2.1s	1061×	body	2048	valid
717.0ms	1823×	body	1024	valid
419.0ms	54×	body	4096	valid
226.0ms	4057×	body	128	valid
145.0ms	698×	body	512	valid
43.0ms	307×	body	256	valid
9.0ms	143×	body	128	invalid
8.0ms	9×	body	2048	invalid
2.0ms	4×	body	8192	exit

Compiler

Compiled 441 to 287 computations (34.9% saved)

Details

analyze893.0ms (11.9%)

sample144.0ms (1.9%)

simplify181.0ms (2.4%)

prune6.0ms (0.1%)

localize17.0ms (0.2%)

rewrite22.0ms (0.3%)

series286.0ms (3.8%)

simplify63.0ms (0.8%)

prune99.0ms (1.3%)

localize11.0ms (0.1%)

rewrite61.0ms (0.8%)

series300.0ms (4%)

simplify124.0ms (1.6%)

prune243.0ms (3.2%)

localize18.0ms (0.2%)

rewrite19.0ms (0.3%)

series65.0ms (0.9%)

simplify60.0ms (0.8%)

prune97.0ms (1.3%)

localize18.0ms (0.2%)

rewrite39.0ms (0.5%)

series70.0ms (0.9%)

simplify67.0ms (0.9%)

prune119.0ms (1.6%)

regimes249.0ms (3.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.2s (56.4%)

Profiling