Details

analyze735.0ms (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
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

22.0ms	63×	body	1024	valid
16.0ms	46×	body	1024	invalid
11.0ms	157×	body	128	valid
6.0ms	27×	body	512	valid
5.0ms	23×	body	512	invalid
3.0ms	18×	body	256	invalid
2.0ms	21×	body	128	invalid
1.0ms	9×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.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))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-r_binary64` `sqrt-prod_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 94

Calls

3 calls:

13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series455.0ms (5.6%)

Counts

3 → 9

Calls

3 calls:

313.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
106.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
36.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify53.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	6032	2380

prune127.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	96	9	105

Merged error: 0b

Counts

105 → 9

Compiler

Compiled 2442 to 959 computations (60.7% saved)

localize19.0ms (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 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
5.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite82.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
102×	`sqrt-prod_binary64`
86×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
78×	`cbrt-prod_binary64`
58×	`associate-r_binary64`
38×	`add-exp-log_binary64`
29×	`add-cbrt-cube_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
9×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-/l*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`associate-r/_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `-commutative_binary64`

Counts

4 → 201

Calls

4 calls:

32.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(/.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)))

series570.0ms (7%)

Counts

4 → 12

Calls

4 calls:

243.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
229.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
53.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
45.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify132.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4946	6988
1	4946	6988

prune376.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	214	8	222

Merged error: 0b

Counts

222 → 8

Compiler

Compiled 8412 to 3731 computations (55.6% saved)

localize16.0ms (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) (/.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))))
0.2b	(/.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)))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

rewrite99.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
111×	`add-sqr-sqrt_binary64`
94×	`cbrt-prod_binary64`
91×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
67×	`associate-r_binary64`
47×	`sqrt-prod_binary64`
32×	`add-exp-log_binary64`
22×	`div-inv_binary64`
20×	`add-cbrt-cube_binary64`
12×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`associate-/r_binary64` `associate-/l_binary64`
7×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/l/_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 225

Calls

4 calls:

31.0ms	(.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))))
16.0ms	(/.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))))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series797.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

334.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
322.0ms	(.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))))
101.0ms	(/.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)))
39.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify148.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4931	8061
1	4931	8061

prune400.0ms (4.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	239	6	245

Merged error: 0b

Counts

245 → 6

Compiler

Compiled 7633 to 4285 computations (43.9% saved)

localize14.0ms (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) (/.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2))))
0.2b	(/.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))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
19×	`associate-r_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
13×	`add-cbrt-cube_binary64`
9×	`associate-/r*_binary64` `sqrt-prod_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 103

Calls

4 calls:

16.0ms	(.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))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series1.0s (12.5%)

Counts

4 → 12

Calls

4 calls:

612.0ms	(.f64 (cos.f64 th) (/.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2))))
290.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2)))
79.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))
36.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4999	2633
1	4999	2633

prune132.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	115	6	121

Merged error: 0b

Counts

121 → 6

Compiler

Compiled 2636 to 1384 computations (47.5% saved)

regimes126.0ms (1.5%)

Compiler: Compiled 1078 to 854 computations (20.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	27
1	19	27

end0.0ms (0%)

sample2.6s (31.7%)

Algorithm

1×

intervals

Results

641.0ms	1821×	body	1024	valid
517.0ms	1510×	body	1024	invalid
368.0ms	4812×	body	128	valid
216.0ms	921×	body	512	valid
181.0ms	777×	body	512	invalid
71.0ms	441×	body	256	valid
61.0ms	401×	body	256	invalid
58.0ms	682×	body	128	invalid
3.0ms	5×	body	2048	valid

Compiler

Compiled 163 to 130 computations (20.2% saved)

Details

analyze735.0ms (9%)

sample78.0ms (1%)

simplify9.0ms (0.1%)

prune5.0ms (0.1%)

localize14.0ms (0.2%)

rewrite34.0ms (0.4%)

series455.0ms (5.6%)

simplify53.0ms (0.7%)

prune127.0ms (1.6%)

localize19.0ms (0.2%)

rewrite82.0ms (1%)

series570.0ms (7%)

simplify132.0ms (1.6%)

prune376.0ms (4.6%)

localize16.0ms (0.2%)

rewrite99.0ms (1.2%)

series797.0ms (9.8%)

simplify148.0ms (1.8%)

prune400.0ms (4.9%)

localize14.0ms (0.2%)

rewrite48.0ms (0.6%)

series1.0s (12.5%)

simplify79.0ms (1%)

prune132.0ms (1.6%)

regimes126.0ms (1.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (31.7%)

Profiling