Details

analyze756.0ms (10.3%)

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)

sample77.0ms (1%)

Algorithm

1×

intervals

Results

21.0ms	61×	body	1024	valid
15.0ms	49×	body	1024	invalid
12.0ms	160×	body	128	valid
7.0ms	31×	body	512	invalid
5.0ms	21×	body	512	valid
2.0ms	14×	body	256	valid
1.0ms	19×	body	128	invalid
1.0ms	9×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify96.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune7.0ms (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

Error

0.3b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.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))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_782`
38×	`times-frac_binary64_766`
32×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
22×	`sqrt-prod_binary64_776` `associate-r_binary64_700`
10×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
6×	`associate-/r*_binary64_704`
5×	`add-log-exp_binary64_799` `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` `flip3-+_binary64_763` `associate-/l/_binary64_707` `div-inv_binary64_757` `flip-+_binary64_734` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
1×	`frac-2neg_binary64_771` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

3 → 94

Calls

3 calls:

13.0ms	(.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))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series232.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

163.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
49.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
20.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4977	2380
1	4977	2380

prune122.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Error

0.0b

Counts

105 → 7

Compiler

Compiled 2425 to 945 computations (61% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
6.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite88.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64_782`
146×	`times-frac_binary64_766`
127×	`sqrt-prod_binary64_776`
90×	`cbrt-prod_binary64_791`
87×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
58×	`associate-r_binary64_700`
27×	`add-exp-log_binary64_798`
21×	`unswap-sqr_binary64_728`
19×	`add-cbrt-cube_binary64_796`
10×	`associate-l_binary64_701`
9×	`associate-/r*_binary64_704`
8×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `div-exp_binary64_811` `pow1_binary64_821`
6×	`sqrt-div_binary64_777` `associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799`
3×	`flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734`
2×	`rem-sqrt-square_binary64_773` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `pow1/2_binary64_840`
1×	`frac-2neg_binary64_771` `associate-l/_binary64_703` `frac-times_binary64_770` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 226

Calls

4 calls:

35.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
12.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series217.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
60.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
24.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
23.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify115.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5181	8434

prune398.0ms (5.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	238	7	245

Error

0.0b

Counts

245 → 7

Compiler

Compiled 9735 to 4502 computations (53.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.4b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_782`
10×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
9×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
6×	`sqrt-prod_binary64_776` `associate-/r*_binary64_704` `times-frac_binary64_766`
5×	`add-log-exp_binary64_799` `pow1_binary64_821`
4×	`associate-*l/_binary64_703`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `associate-r_binary64_700` `associate-l_binary64_701`
2×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `associate-/l/_binary64_707` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
1×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `div-inv_binary64_757` `associate-/l_binary64_705` `+-commutative_binary64_690` `sum-log_binary64_851` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

3 → 60

Calls

3 calls:

9.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series213.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

125.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
67.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
20.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4932	1303
1	4932	1303

prune64.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	69	7	76

Error

Counts

76 → 7

Compiler

Compiled 1399 to 541 computations (61.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))
0.3b	(/.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)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))

rewrite60.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64_782`
70×	`times-frac_binary64_766`
49×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
46×	`cbrt-prod_binary64_791`
32×	`add-exp-log_binary64_798`
31×	`associate-r_binary64_700`
23×	`sqrt-prod_binary64_776`
22×	`add-cbrt-cube_binary64_796`
10×	`cbrt-undiv_binary64_794` `associate-/r*_binary64_704` `div-exp_binary64_811`
9×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
8×	`unswap-sqr_binary64_728`
7×	`associate-l_binary64_701`
6×	`add-log-exp_binary64_799` `associate-/l*_binary64_705` `pow1_binary64_821`
4×	`div-inv_binary64_757`
2×	`frac-2neg_binary64_771` `flip3-+_binary64_763` `associate-/l/_binary64_707` `flip-+_binary64_734` `clear-num_binary64_759`
1×	`associate-l/_binary64_703` `frac-times_binary64_770` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 155

Calls

4 calls:

23.0ms	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (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))))
6.0ms	(/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series434.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
133.0ms	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
110.0ms	(/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))
22.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify118.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4942	4311
1	4942	4311

prune230.0ms (3.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	167	7	174

Error

Counts

174 → 7

Compiler

Compiled 4649 to 2630 computations (43.4% saved)

regimes664.0ms (9%)

Accuracy

Total 0.4b remaining (94.6%)

Threshold costs 0.4b (94.6%)

Compiler

Compiled 8538 to 6207 computations (27.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	20
1	13	20

end0.0ms (0%)

sample3.2s (43.6%)

Algorithm

1×

intervals

Results

571.0ms	1835×	body	1024	valid
454.0ms	1462×	body	1024	invalid
372.0ms	4857×	body	128	valid
203.0ms	911×	body	512	valid
178.0ms	775×	body	512	invalid
64.0ms	392×	body	256	valid
55.0ms	347×	body	256	invalid
46.0ms	579×	body	128	invalid
2.0ms	5×	body	2048	valid

Compiler

Compiled 1085 to 789 computations (27.3% saved)

Details

analyze756.0ms (10.3%)

sample77.0ms (1%)

simplify96.0ms (1.3%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite33.0ms (0.4%)

series232.0ms (3.1%)

simplify75.0ms (1%)

prune122.0ms (1.7%)

localize16.0ms (0.2%)

rewrite88.0ms (1.2%)

series217.0ms (2.9%)

simplify115.0ms (1.6%)

prune398.0ms (5.4%)

localize10.0ms (0.1%)

rewrite24.0ms (0.3%)

series213.0ms (2.9%)

simplify84.0ms (1.1%)

prune64.0ms (0.9%)

localize15.0ms (0.2%)

rewrite60.0ms (0.8%)

series434.0ms (5.9%)

simplify118.0ms (1.6%)

prune230.0ms (3.1%)

regimes664.0ms (9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.2s (43.6%)

Profiling