Details

analyze748.0ms (9.6%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 20 to 16 computations (20% saved)

sample78.0ms (1%)

Algorithm

1×

intervals

Results

18.0ms	60×	body	1024	valid
14.0ms	48×	body	1024	invalid
11.0ms	147×	body	128	valid
10.0ms	34×	body	512	valid
4.0ms	20×	body	512	invalid
3.0ms	21×	body	256	invalid
2.0ms	15×	body	256	valid
2.0ms	25×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify91.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune5.0ms (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: 0.7b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.4b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_782`
38×	`times-frac_binary64_766`
31×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
22×	`sqrt-prod_binary64_776` `associate-r_binary64_700`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
6×	`associate-/r*_binary64_704`
4×	`pow1_binary64_821`
3×	`unswap-sqr_binary64_728` `associate-/l_binary64_705` `associate-l*_binary64_701`
2×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `associate-/l/_binary64_707` `add-log-exp_binary64_799` `div-inv_binary64_757` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
1×	`frac-2neg_binary64_771` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

2 → 83

Calls

2 calls:

12.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series218.0ms (2.8%)

Counts

2 → 6

Calls

2 calls:

168.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
50.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4971	2187
1	4971	2187

prune113.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 0.3b

Counts

91 → 9

Compiler

Compiled 2218 to 885 computations (60.1% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

0.3b

(/.f64 (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

0.4b

(*.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))

rewrite88.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64_766`
110×	`add-sqr-sqrt_binary64_782`
94×	`cbrt-prod_binary64_791`
90×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
67×	`associate-r_binary64_700`
47×	`sqrt-prod_binary64_776`
31×	`add-exp-log_binary64_798`
22×	`div-inv_binary64_757`
19×	`add-cbrt-cube_binary64_796`
12×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
10×	`associate-/r_binary64_704` `associate-/l_binary64_705`
7×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
5×	`pow1_binary64_821`
3×	`associate-/l/_binary64_707` `add-log-exp_binary64_799` `associate-l_binary64_701`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`flip3-+_binary64_763` `flip-+_binary64_734` `associate-r/_binary64_702` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

3 → 214

Calls

3 calls:

30.0ms

(*.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))

14.0ms

(/.f64 (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

11.0ms

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

series386.0ms (5%)

Counts

3 → 9

Calls

3 calls:

171.0ms

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

160.0ms

(*.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))

55.0ms

(/.f64 (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

simplify136.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4938	7868
1	4938	7868

prune361.0ms (4.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	223	9	232

Merged error: 0.3b

Counts

232 → 9

Compiler

Compiled 7313 to 4109 computations (43.8% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.3b

(/.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2)))

0.4b

(*.f64 (cos.f64 th) (/.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2))))

0.4b

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_782`
22×	`cbrt-prod_binary64_791`
19×	`add-exp-log_binary64_798` `associate-r_binary64_700`
18×	`times-frac_binary64_766`
17×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
12×	`add-cbrt-cube_binary64_796`
9×	`sqrt-prod_binary64_776` `associate-/r*_binary64_704`
7×	`pow1_binary64_821`
6×	`prod-exp_binary64_809` `associate-l_binary64_701` `cbrt-unprod_binary64_793`
4×	`cbrt-undiv_binary64_794` `associate-*l/_binary64_703` `div-exp_binary64_811`
3×	`unswap-sqr_binary64_728` `add-log-exp_binary64_799`
2×	`flip3-+_binary64_763` `associate-/l/_binary64_707` `div-inv_binary64_757` `flip-+_binary64_734` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`frac-2neg_binary64_771` `associate-/l_binary64_705` `associate-r/_binary64_702` `clear-num_binary64_759`

Counts

3 → 92

Calls

3 calls:

13.0ms

(*.f64 (cos.f64 th) (/.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2))))

10.0ms

(/.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2)))

8.0ms

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

series527.0ms (6.8%)

Counts

3 → 9

Calls

3 calls:

327.0ms

(*.f64 (cos.f64 th) (/.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2))))

157.0ms

(/.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2)))

43.0ms

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5085	2440

prune125.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	104	6	110

Merged error: 0.3b

Counts

110 → 6

Compiler

Compiled 2442 to 1325 computations (45.7% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.3b

(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))

0.3b

(*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th))

0.4b

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_798`
17×	`add-sqr-sqrt_binary64_782`
16×	`cbrt-prod_binary64_791`
13×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796`
10×	`associate-*l/_binary64_703` `pow1_binary64_821`
9×	`associate-/r_binary64_704` `associate-r*_binary64_700` `times-frac_binary64_766`
7×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
6×	`sqrt-prod_binary64_776`
4×	`associate-l_binary64_701` `pow-prod-down_binary64_831`
3×	`cbrt-undiv_binary64_794` `flip3-+_binary64_763` `add-log-exp_binary64_799` `flip-+_binary64_734` `div-exp_binary64_811`
2×	`unswap-sqr_binary64_728` `associate-/l/_binary64_707` `*-commutative_binary64_691`
1×	`frac-2neg_binary64_771` `div-inv_binary64_757` `associate-/l*_binary64_705` `clear-num_binary64_759`

Counts

3 → 81

Calls

3 calls:

12.0ms

(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))

9.0ms

(*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th))

8.0ms

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

series399.0ms (5.1%)

Counts

3 → 9

Calls

3 calls:

248.0ms

(/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))

108.0ms

(*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th))

43.0ms

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4976	2160
1	4976	2160

prune99.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	90	6	96

Merged error: 0.3b

Counts

96 → 6

Compiler

Compiled 2054 to 1073 computations (47.8% saved)

regimes721.0ms (9.3%)

Compiler: Compiled 8785 to 6479 computations (26.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	27
1	19	27

end0.0ms (0%)

sample3.3s (42.3%)

Algorithm

1×

intervals

Results

558.0ms	1794×	body	1024	valid
492.0ms	1632×	body	1024	invalid
370.0ms	4823×	body	128	valid
210.0ms	920×	body	512	valid
168.0ms	763×	body	512	invalid
69.0ms	460×	body	256	valid
59.0ms	387×	body	256	invalid
53.0ms	656×	body	128	invalid
1.0ms	3×	body	2048	valid

Compiler

Compiled 1119 to 826 computations (26.2% saved)

Details

analyze748.0ms (9.6%)

sample78.0ms (1%)

simplify91.0ms (1.2%)

prune5.0ms (0.1%)

localize13.0ms (0.2%)

rewrite27.0ms (0.4%)

series218.0ms (2.8%)

simplify84.0ms (1.1%)

prune113.0ms (1.5%)

localize15.0ms (0.2%)

rewrite88.0ms (1.1%)

series386.0ms (5%)

simplify136.0ms (1.7%)

prune361.0ms (4.6%)

localize14.0ms (0.2%)

rewrite38.0ms (0.5%)

series527.0ms (6.8%)

simplify81.0ms (1%)

prune125.0ms (1.6%)

localize13.0ms (0.2%)

rewrite41.0ms (0.5%)

series399.0ms (5.1%)

simplify63.0ms (0.8%)

prune99.0ms (1.3%)

regimes721.0ms (9.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (42.3%)

Profiling