Details

analyze80.0ms (2.9%)

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
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)

sample18.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify42.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5126	25

prune6.0ms (0.2%)

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

rewrite31.0ms (1.1%)

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:

9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
6.0ms	(.f64 4 (.f64 b b))
6.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
5.0ms	(+.f64 (.f64 a a) (.f64 b b))

series221.0ms (8%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
52.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
42.0ms	(+.f64 (.f64 a a) (.f64 b b))
38.0ms	(.f64 4 (.f64 b b))

simplify71.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4923	1108
1	4923	1108

prune198.0ms (7.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

Compiler

Compiled 4056 to 2243 computations (44.7% saved)

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 4 (.f64 b b))
0.0b	(+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 a 4) (pow.f64 b 4)))
0.0b	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 a 4) (pow.f64 b 4))) (.f64 4 (.f64 b b)))
3.2b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

rewrite68.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

23.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 a 4) (pow.f64 b 4))) (.f64 4 (.f64 b b)))
19.0ms	(+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 a 4) (pow.f64 b 4)))
11.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
6.0ms	(.f64 4 (.f64 b b))

series252.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(+.f64 (+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 a 4) (pow.f64 b 4))) (.f64 4 (.f64 b b)))
72.0ms	(+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 a 4) (pow.f64 b 4)))
57.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
33.0ms	(.f64 4 (.f64 b b))

simplify64.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4975	1703
1	4975	1703

prune124.0ms (4.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0.0b

Counts

90 → 4

Compiler

Compiled 2627 to 1707 computations (35% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))) 2) (.f64 4 (*.f64 b b)))
0.3b	(pow.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (+.f64 (.f64 a a) (*.f64 b b)))) 2)
11.6b	(sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
11.6b	(sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

rewrite41.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64`
14×	`pow-pow_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `sqrt-prod_binary64`
5×	`pow-prod-up_binary64`
4×	`add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow-unpow_binary64` `pow-sqr_binary64` `flip-+_binary64`
2×	`rem-sqrt-square_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `sqrt-pow2_binary64` `unpow2_binary64` `sqr-pow_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64`

Counts

4 → 72

Calls

4 calls:

15.0ms	(pow.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (+.f64 (.f64 a a) (*.f64 b b)))) 2)
9.0ms	(+.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))) 2) (.f64 4 (*.f64 b b)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

series236.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(+.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))) 2) (.f64 4 (*.f64 b b)))
58.0ms	(pow.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (+.f64 (.f64 a a) (*.f64 b b)))) 2)
48.0ms	(sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
42.0ms	(sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

simplify49.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5195	1233

prune97.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

Compiler

Compiled 2523 to 976 computations (61.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.0b	(pow.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
0.0b	(+.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (.f64 4 (.f64 b b)))
11.6b	(sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`add-exp-log_binary64`
4×	`add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `pow-pow_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `+-commutative_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `sqrt-pow2_binary64` `sqr-pow_binary64` `rem-sqrt-square_binary64` `pow-exp_binary64`

Counts

4 → 60

Calls

4 calls:

11.0ms	(+.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (.f64 4 (.f64 b b)))
6.0ms	(pow.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
5.0ms	(+.f64 (.f64 a a) (.f64 b b))
5.0ms	(sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))

series245.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(pow.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4)
77.0ms	(+.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 a a) (.f64 b b))) 4) (.f64 4 (.f64 b b)))
53.0ms	(sqrt.f64 (+.f64 (.f64 a a) (.f64 b b)))
37.0ms	(+.f64 (.f64 a a) (.f64 b b))

simplify57.0ms (2%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5467	1281

prune85.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	72	4	76

Merged error: 0.0b

Counts

76 → 4

Compiler

Compiled 1923 to 897 computations (53.4% saved)

regimes50.0ms (1.8%)

Compiler: Compiled 512 to 320 computations (37.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	27
1	26	27

end0.0ms (0%)

sample653.0ms (23.5%)

Algorithm

1×

intervals

Results

367.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 160 to 103 computations (35.6% saved)

Details

analyze80.0ms (2.9%)

sample18.0ms (0.7%)

simplify42.0ms (1.5%)

prune6.0ms (0.2%)

localize10.0ms (0.4%)

rewrite31.0ms (1.1%)

series221.0ms (8%)

simplify71.0ms (2.6%)

prune198.0ms (7.1%)

localize16.0ms (0.6%)

rewrite68.0ms (2.5%)

series252.0ms (9.1%)

simplify64.0ms (2.3%)

prune124.0ms (4.5%)

localize12.0ms (0.5%)

rewrite41.0ms (1.5%)

series236.0ms (8.5%)

simplify49.0ms (1.8%)

prune97.0ms (3.5%)

localize11.0ms (0.4%)

rewrite32.0ms (1.1%)

series245.0ms (8.8%)

simplify57.0ms (2%)

prune85.0ms (3.1%)

regimes50.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample653.0ms (23.5%)

Profiling