Details

analyze126.0ms (2.8%)

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%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	80	valid
0.0ms	1×	body	80	invalid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5073	43

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 58 to 38 computations (34.5% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.4b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite48.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-*r/_binary64`
17×	`pow1_binary64` `add-exp-log_binary64` `add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
10×	`add-cube-cbrt_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`associate-l_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `frac-add_binary64` `insert-posit16` `flip-+_binary64`
3×	`pow-unpow_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `flip--_binary64` `*-commutative_binary64`
2×	`sub-neg_binary64` `difference-of-squares_binary64`
1×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-out--_binary64` `pow-exp_binary64`

Counts

4 → 98

Calls

4 calls:

17.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
11.0ms	(.f64 (.f64 a a) (-.f64 1 a))
10.0ms	(.f64 (.f64 b b) (+.f64 3 a))
6.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series270.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
73.0ms	(.f64 (.f64 a a) (-.f64 1 a))
62.0ms	(.f64 (.f64 b b) (+.f64 3 a))
56.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify141.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4992	1938
1	4992	1938

prune169.0ms (3.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	108	3	111

Merged error: 0.0b

Counts

111 → 3

Compiler

Compiled 3943 to 2053 computations (47.9% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
0.1b	(.f64 (.f64 a a) (-.f64 1 a))
0.4b	(.f64 (.f64 b b) (+.f64 3 a))
2.2b	(.f64 (.f64 b b) (*.f64 a a))

rewrite54.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`pow1_binary64`
28×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`pow-prod-down_binary64`
18×	`associate-*r/_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
14×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow-prod-up_binary64` `frac-add_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `insert-posit16` `flip-+_binary64` `*-commutative_binary64`
3×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `difference-of-squares_binary64` `pow-sqr_binary64` `pow2_binary64`
1×	`distribute-lft-out_binary64` `distribute-lft-out--_binary64`

Counts

4 → 109

Calls

4 calls:

17.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
11.0ms	(.f64 (.f64 a a) (-.f64 1 a))
11.0ms	(.f64 (.f64 b b) (*.f64 a a))
10.0ms	(.f64 (.f64 b b) (+.f64 3 a))

series251.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
68.0ms	(.f64 (.f64 a a) (-.f64 1 a))
53.0ms	(.f64 (.f64 b b) (*.f64 a a))
47.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify180.0ms (4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	4932	1844
1	4932	1844

prune233.0ms (5.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	121	3	124

Merged error: 0.0b

Counts

124 → 3

Compiler

Compiled 5145 to 2958 computations (42.5% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (.f64 (.f64 b b) (.f64 a a)))
0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (-.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a 4))) (.f64 (pow.f64 a 3) 4)))
0.4b	(.f64 (.f64 b b) (+.f64 12 (*.f64 a 4)))
2.2b	(.f64 (.f64 b b) (*.f64 a a))

rewrite79.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`pow1_binary64`
39×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
30×	`pow-prod-down_binary64`
25×	`add-log-exp_binary64`
24×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`sum-log_binary64`
8×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`associate-r_binary64` `associate-l_binary64`
4×	`flip3-+_binary64` `pow-prod-up_binary64` `frac-add_binary64` `pow-plus_binary64` `insert-posit16` `flip-+_binary64`
3×	`diff-log_binary64` `associate-+r+_binary64` `*-commutative_binary64`
2×	`flip3--_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `flip--_binary64` `pow2_binary64` `associate--l+_binary64`
1×	`sub-neg_binary64` `associate-+r-_binary64` `distribute-lft-out_binary64` `associate-+l+_binary64` `+-commutative_binary64`

Counts

4 → 109

Calls

4 calls:

39.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (-.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a 4))) (.f64 (pow.f64 a 3) 4)))
15.0ms	(.f64 2 (.f64 (.f64 b b) (.f64 a a)))
11.0ms	(.f64 (.f64 b b) (*.f64 a a))
9.0ms	(.f64 (.f64 b b) (+.f64 12 (*.f64 a 4)))

series300.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (-.f64 (.f64 (.f64 b b) (+.f64 12 (.f64 a 4))) (.f64 (pow.f64 a 3) 4)))
64.0ms	(.f64 (.f64 b b) (+.f64 12 (*.f64 a 4)))
56.0ms	(.f64 2 (.f64 (.f64 b b) (.f64 a a)))
56.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify133.0ms (3%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4946	3149
1	4946	3149

prune251.0ms (5.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	120	4	124

Merged error: 0.0b

Counts

124 → 4

Compiler

Compiled 5120 to 3317 computations (35.2% saved)

localize26.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (*.f64 a 4))))
0.5b	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (*.f64 a 4))))
10.2b	(sqrt.f64 (+.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (-.f64 (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (.f64 a 4)))) (.f64 (pow.f64 a 3) 4))))
10.2b	(sqrt.f64 (+.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (-.f64 (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (.f64 a 4)))) (.f64 (pow.f64 a 3) 4))))

rewrite96.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
16×	`pow1_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64` `sqrt-div_binary64`
10×	`sqrt-prod_binary64`
8×	`flip3-+_binary64` `frac-add_binary64` `add-cube-cbrt_binary64` `flip-+_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `associate-*r/_binary64` `insert-posit16` `flip--_binary64`
2×	`pow1/2_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`

Counts

4 → 92

Calls

4 calls:

30.0ms	(sqrt.f64 (+.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (-.f64 (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (.f64 a 4)))) (.f64 (pow.f64 a 3) 4))))
29.0ms	(sqrt.f64 (+.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (-.f64 (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (.f64 a 4)))) (.f64 (pow.f64 a 3) 4))))
18.0ms	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (*.f64 a 4))))
16.0ms	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (*.f64 a 4))))

series476.0ms (10.7%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(sqrt.f64 (+.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (-.f64 (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (.f64 a 4)))) (.f64 (pow.f64 a 3) 4))))
158.0ms	(sqrt.f64 (+.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (-.f64 (.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (.f64 a 4)))) (.f64 (pow.f64 a 3) 4))))
77.0ms	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (*.f64 a 4))))
77.0ms	(.f64 (.f64 b b) (+.f64 (.f64 (.f64 a a) 2) (+.f64 12 (*.f64 a 4))))

simplify94.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5257	4718

prune440.0ms (9.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	104	4	108

Merged error: 0.0b

Counts

108 → 4

Compiler

Compiled 8040 to 5679 computations (29.4% saved)

regimes86.0ms (1.9%)

Compiler: Compiled 907 to 646 computations (28.8% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	43
1	47	43

end0.0ms (0%)

sample835.0ms (18.8%)

Algorithm

1×

intervals

Results

518.0ms	8000×	body	80	valid
0.0ms	4×	body	80	invalid

Compiler

Compiled 216 to 153 computations (29.2% saved)

Details

analyze126.0ms (2.8%)

sample24.0ms (0.5%)

simplify66.0ms (1.5%)

prune3.0ms (0.1%)

localize16.0ms (0.4%)

rewrite48.0ms (1.1%)

series270.0ms (6.1%)

simplify141.0ms (3.2%)

prune169.0ms (3.8%)

localize20.0ms (0.5%)

rewrite54.0ms (1.2%)

series251.0ms (5.6%)

simplify180.0ms (4%)

prune233.0ms (5.2%)

localize23.0ms (0.5%)

rewrite79.0ms (1.8%)

series300.0ms (6.7%)

simplify133.0ms (3%)

prune251.0ms (5.6%)

localize26.0ms (0.6%)

rewrite96.0ms (2.2%)

series476.0ms (10.7%)

simplify94.0ms (2.1%)

prune440.0ms (9.9%)

regimes86.0ms (1.9%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample835.0ms (18.8%)

Profiling