Details

analyze85.0ms (3.8%)

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample19.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify41.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5044	25

prune2.0ms (0.1%)

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: 0.2b

Counts

2 → 1

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.0b	(.f64 4 (.f64 b b))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite28.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64` `add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
2×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `associate-r_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 59

Calls

4 calls:

8.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
6.0ms	(.f64 4 (.f64 b b))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
4.0ms	(+.f64 (.f64 a a) (.f64 b b))

series216.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
49.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
40.0ms	(.f64 4 (.f64 b b))
40.0ms	(+.f64 (.f64 a a) (.f64 b b))

simplify47.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4931	1108
1	4931	1108

prune82.0ms (3.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	2	72

Merged error: 0b

Counts

72 → 2

Compiler

Compiled 1611 to 763 computations (52.6% saved)

localize16.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 b 4) (pow.f64 a 4))
0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
2.8b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

rewrite54.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
15×	`add-log-exp_binary64`
9×	`*-un-lft-identity_binary64`
7×	`sum-log_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`associate-l_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `unpow-prod-down_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`associate-+l+_binary64` `unswap-sqr_binary64`

Counts

4 → 74

Calls

4 calls:

22.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
11.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
7.0ms	(+.f64 (pow.f64 b 4) (pow.f64 a 4))
6.0ms	(.f64 4 (.f64 b b))

series235.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (.f64 b b)))
62.0ms	(+.f64 (pow.f64 b 4) (pow.f64 a 4))
51.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
38.0ms	(.f64 4 (.f64 b b))

simplify78.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5059	1404

prune117.0ms (5.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	86	2	88

Merged error: 0b

Counts

88 → 2

Compiler

Compiled 2486 to 1628 computations (34.5% saved)

localize15.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
15.9b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
15.9b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))

rewrite35.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-exp-log_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `pow1/2_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 66

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series318.0ms (14.2%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
106.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
56.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
48.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify42.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5004	1752

prune116.0ms (5.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	78	2	80

Merged error: 0b

Counts

80 → 2

Compiler

Compiled 3266 to 1451 computations (55.6% saved)

regimes36.0ms (1.6%)

Compiler: Compiled 256 to 176 computations (31.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	37
1	35	37

end0.0ms (0%)

sample638.0ms (28.6%)

Algorithm

1×

intervals

Results

385.0ms	8000×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 103 to 73 computations (29.1% saved)

Details

analyze85.0ms (3.8%)

sample19.0ms (0.8%)

simplify41.0ms (1.8%)

prune2.0ms (0.1%)

localize10.0ms (0.4%)

rewrite28.0ms (1.3%)

series216.0ms (9.7%)

simplify47.0ms (2.1%)

prune82.0ms (3.7%)

localize16.0ms (0.7%)

rewrite54.0ms (2.4%)

series235.0ms (10.5%)

simplify78.0ms (3.5%)

prune117.0ms (5.3%)

localize15.0ms (0.7%)

rewrite35.0ms (1.6%)

series318.0ms (14.2%)

simplify42.0ms (1.9%)

prune116.0ms (5.2%)

regimes36.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample638.0ms (28.6%)

Profiling