Details

analyze76.0ms (2.1%)

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)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	80	valid
0.0ms	1×	body	80	invalid

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify71.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5045	25

prune3.0ms (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 (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite30.0ms (0.8%)

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`
4×	`insert-posit16`
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 → 63

Calls

4 calls:

10.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
7.0ms	(.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))

series206.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
51.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
37.0ms	(+.f64 (.f64 a a) (.f64 b b))
37.0ms	(.f64 4 (.f64 b b))

simplify83.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4937	1168
1	4937	1168

prune86.0ms (2.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	3	76

Merged error: 0.0b

Counts

76 → 3

Compiler

Compiled 1720 to 819 computations (52.4% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.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))
2.2b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

rewrite75.0ms (2.1%)

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` `insert-posit16`
2×	`flip3-+_binary64` `associate-r_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`associate-+l+_binary64` `unswap-sqr_binary64` `associate-+r+_binary64`

Counts

4 → 78

Calls

4 calls:

31.0ms	(+.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)))
21.0ms	(+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
12.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
7.0ms	(.f64 4 (.f64 b b))

series261.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(+.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)))
70.0ms	(+.f64 (.f64 (.f64 a a) (.f64 b (.f64 b 2))) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))
57.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
41.0ms	(.f64 4 (.f64 b b))

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5074	1791

prune135.0ms (3.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	90	3	93

Merged error: 0.0b

Counts

93 → 3

Compiler

Compiled 2698 to 1759 computations (34.8% saved)

localize13.0ms (0.4%)

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)
12.0b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
12.0b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))

rewrite34.0ms (0.9%)

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` `insert-posit16` `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 → 70

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
7.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
6.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series341.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
114.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
57.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
55.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5008	1834

prune127.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	82	3	85

Merged error: 0.0b

Counts

85 → 3

Compiler

Compiled 3447 to 1539 computations (55.4% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (*.f64 16 (pow.f64 b 4)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
34.6b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))

rewrite45.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
8×	`add-exp-log_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
4×	`insert-posit16`
3×	`associate-/r_binary64` `flip3--_binary64` `associate-/l_binary64` `flip--_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 82

Calls

4 calls:

19.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))
9.0ms	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (*.f64 16 (pow.f64 b 4)))
8.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
6.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series828.0ms (23.1%)

Counts

4 → 12

Calls

4 calls:

322.0ms	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (*.f64 16 (pow.f64 b 4)))
298.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))
154.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
52.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify110.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4971	3018
1	4971	3018

prune152.0ms (4.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	94	3	97

Merged error: 0b

Counts

97 → 3

Compiler

Compiled 3886 to 1870 computations (51.9% saved)

regimes51.0ms (1.4%)

Compiler: Compiled 392 to 282 computations (28.1% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	37
1	36	37

end0.0ms (0%)

sample650.0ms (18.2%)

Algorithm

1×

intervals

Results

387.0ms	8000×	body	80	valid
0.0ms	4×	body	80	invalid

Compiler

Compiled 122 to 89 computations (27% saved)

Details

analyze76.0ms (2.1%)

sample20.0ms (0.5%)

simplify71.0ms (2%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

rewrite30.0ms (0.8%)

series206.0ms (5.8%)

simplify83.0ms (2.3%)

prune86.0ms (2.4%)

localize16.0ms (0.5%)

rewrite75.0ms (2.1%)

series261.0ms (7.3%)

simplify65.0ms (1.8%)

prune135.0ms (3.8%)

localize13.0ms (0.4%)

rewrite34.0ms (0.9%)

series341.0ms (9.5%)

simplify65.0ms (1.8%)

prune127.0ms (3.6%)

localize17.0ms (0.5%)

rewrite45.0ms (1.3%)

series828.0ms (23.1%)

simplify110.0ms (3.1%)

prune152.0ms (4.3%)

regimes51.0ms (1.4%)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

end0.0ms (0%)

sample650.0ms (18.2%)

Profiling