Details

analyze136.0ms (1.4%)

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%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 22 computations (31.3% saved)

sample25.0ms (0.3%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4975	46
1	4975	46

prune3.0ms (0%)

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 62 to 42 computations (32.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite42.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64` `add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-*r/_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 82

Calls

4 calls:

12.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
11.0ms	(.f64 (.f64 a a) (+.f64 1 a))
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
6.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series351.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
73.0ms	(.f64 (.f64 a a) (+.f64 1 a))
70.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
59.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4977	1907
1	4977	1907

prune158.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	4	95

Merged error: 0b

Counts

95 → 4

Compiler

Compiled 3643 to 1971 computations (45.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (.f64 (.f64 a a) (.f64 b b)))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
1.9b	(.f64 (.f64 a a) (*.f64 b b))

rewrite54.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`pow1_binary64`
44×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
33×	`pow-prod-down_binary64`
27×	`cbrt-unprod_binary64` `prod-exp_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`add-log-exp_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-plus_binary64` `insert-posit16` `-commutative_binary64`
3×	`unswap-sqr_binary64`
2×	`sub-neg_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-sqr_binary64` `pow2_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 107

Calls

4 calls:

16.0ms	(.f64 2 (.f64 (.f64 a a) (.f64 b b)))
11.0ms	(.f64 (.f64 a a) (*.f64 b b))
11.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
10.0ms	(.f64 (.f64 a a) (+.f64 1 a))

series252.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(.f64 (.f64 a a) (+.f64 1 a))
67.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
59.0ms	(.f64 2 (.f64 (.f64 a a) (.f64 b b)))
56.0ms	(.f64 (.f64 a a) (*.f64 b b))

simplify125.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4984	1391
1	4984	1391

prune235.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	119	4	123

Merged error: 0b

Counts

123 → 4

Compiler

Compiled 5129 to 3066 computations (40.2% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
3.6b	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) 16)))
31.0b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) 16))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))))))

rewrite47.0ms (0.5%)

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:

21.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) 16))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))))))
10.0ms	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) 16)))
7.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
7.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series1.5s (15.4%)

Counts

4 → 12

Calls

4 calls:

696.0ms	(-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) 16)))
593.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) 16))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))))))
160.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
60.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5713	7083

prune359.0ms (3.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	94	4	98

Merged error: 0b

Counts

98 → 4

Compiler

Compiled 9355 to 4931 computations (47.3% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.8b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3))
6.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2)))))
41.0b	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3)) (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))

rewrite64.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
16×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
15×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`times-frac_binary64` `associate-+r+_binary64`
8×	`add-log-exp_binary64` `associate--l+_binary64`
7×	`add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `sub-neg_binary64` `associate-/l*_binary64` `insert-posit16` `flip-+_binary64`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `unpow-prod-down_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64`

Counts

4 → 92

Calls

4 calls:

25.0ms	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3)) (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))
14.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2)))))
14.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3))
7.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series4.5s (45.8%)

Counts

4 → 12

Calls

4 calls:

2.2s	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3))
1.2s	(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6) (pow.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) 3)) (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2))))))
984.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 4 (.f64 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1))) (-.f64 (.f64 4 (+.f64 (.f64 (.f64 b b) (-.f64 1 (.f64 a 3))) (.f64 (.f64 a a) (+.f64 a 1)))) (pow.f64 (+.f64 (.f64 a a) (*.f64 b b)) 2)))))
56.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify149.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4947	10282
1	4947	10282

prune486.0ms (5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	104	4	108

Merged error: 0b

Counts

108 → 4

Compiler

Compiled 12377 to 6484 computations (47.6% saved)

regimes107.0ms (1.1%)

Compiler: Compiled 1549 to 955 computations (38.3% saved)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	78	58
1	78	58

end0.0ms (0%)

sample871.0ms (8.9%)

Algorithm

1×

intervals

Results

527.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Compiler

Compiled 313 to 198 computations (36.7% saved)

Details

analyze136.0ms (1.4%)

sample25.0ms (0.3%)

simplify67.0ms (0.7%)

prune3.0ms (0%)

localize19.0ms (0.2%)

rewrite42.0ms (0.4%)

series351.0ms (3.6%)

simplify65.0ms (0.7%)

prune158.0ms (1.6%)

localize21.0ms (0.2%)

rewrite54.0ms (0.6%)

series252.0ms (2.6%)

simplify125.0ms (1.3%)

prune235.0ms (2.4%)

localize29.0ms (0.3%)

rewrite47.0ms (0.5%)

series1.5s (15.4%)

simplify97.0ms (1%)

prune359.0ms (3.7%)

localize34.0ms (0.3%)

rewrite64.0ms (0.7%)

series4.5s (45.8%)

simplify149.0ms (1.5%)

prune486.0ms (5%)

regimes107.0ms (1.1%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample871.0ms (8.9%)

Profiling