Details

analyze144.0ms (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%	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 (0.6%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify231.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4912	46
1	4912	46

prune4.0ms (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: 0.1b

Counts

2 → 1

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize17.0ms (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 1 (.f64 3 a)))))
0.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite52.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-*r/_binary64_1741`
17×	`pow1_binary64_1860` `add-exp-log_binary64_1837`
16×	`add-cbrt-cube_binary64_1835`
14×	`add-sqr-sqrt_binary64_1821`
12×	`*-un-lft-identity_binary64_1799`
10×	`add-cube-cbrt_binary64_1834` `associate-r_binary64_1739`
7×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870`
5×	`associate-l_binary64_1740`
4×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `add-log-exp_binary64_1838` `flip3-+_binary64_1802` `frac-add_binary64_1807` `flip-+_binary64_1773`
3×	`pow-unpow_binary64_1876` `unswap-sqr_binary64_1767` `unpow-prod-down_binary64_1878` `flip--_binary64_1774` `flip3--_binary64_1803` `*-commutative_binary64_1730`
2×	`sub-neg_binary64_1792` `cancel-sign-sub-inv_binary64_1765`
1×	`unpow2_binary64_1864` `pow-to-exp_binary64_1868` `pow-exp_binary64_1867` `sqr-pow_binary64_1771` `pow-pow_binary64_1871` `distribute-lft-out_binary64_1750`

Counts

4 → 93

Calls

4 calls:

15.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))
10.0ms	(.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)

series260.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))
64.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
63.0ms	(.f64 (.f64 a a) (+.f64 1 a))
56.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify66.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5377	2040

prune217.0ms (5.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	3	106

Merged error: 0b

Counts

106 → 3

Compiler

Compiled 5166 to 2961 computations (42.7% saved)

localize21.0ms (0.6%)

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 1 (.f64 3 a)))))
0.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
1.6b	(.f64 (.f64 a a) (*.f64 b b))

rewrite58.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`pow1_binary64_1860`
28×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
21×	`pow-prod-down_binary64_1870`
18×	`associate-*r/_binary64_1741`
15×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
12×	`add-sqr-sqrt_binary64_1821`
11×	`associate-r_binary64_1739`
10×	`*-un-lft-identity_binary64_1799`
8×	`add-cube-cbrt_binary64_1834`
6×	`associate-l_binary64_1740`
4×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `add-log-exp_binary64_1838` `unswap-sqr_binary64_1767` `pow-prod-up_binary64_1869` `*-commutative_binary64_1730` `pow-plus_binary64_1862` `flip3-+_binary64_1802` `frac-add_binary64_1807` `flip-+_binary64_1773`
3×	`flip--_binary64_1774` `flip3--_binary64_1803`
2×	`pow2_binary64_1880` `pow-sqr_binary64_1772` `sub-neg_binary64_1792` `cancel-sign-sub-inv_binary64_1765`
1×	`distribute-lft-out_binary64_1750`

Counts

4 → 104

Calls

4 calls:

14.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))
10.0ms	(.f64 (.f64 a a) (*.f64 b b))
10.0ms	(.f64 (.f64 a a) (+.f64 1 a))
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series253.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))
69.0ms	(.f64 (.f64 a a) (+.f64 1 a))
62.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
50.0ms	(.f64 (.f64 a a) (*.f64 b b))

simplify68.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5160	1949

prune250.0ms (6.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	116	3	119

Merged error: 0b

Counts

119 → 3

Compiler

Compiled 5510 to 3326 computations (39.6% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 a 4) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 b b) (.f64 (.f64 a a) (+.f64 a 1)))))
0.0b	(.f64 4 (+.f64 (.f64 b b) (.f64 (.f64 a a) (+.f64 a 1))))
0.1b	(.f64 (.f64 a a) (+.f64 a 1))
1.6b	(.f64 (.f64 a a) (*.f64 b b))

rewrite68.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`pow1_binary64_1860`
23×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
18×	`pow-prod-down_binary64_1870`
13×	`add-log-exp_binary64_1838`
12×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
10×	`add-sqr-sqrt_binary64_1821`
9×	`*-un-lft-identity_binary64_1799`
8×	`associate-r/_binary64_1741` `associate-r*_binary64_1739`
7×	`add-cube-cbrt_binary64_1834` `flip3-+_binary64_1802` `flip-+_binary64_1773`
6×	`sum-log_binary64_1890`
5×	`associate-l_binary64_1740`
4×	`pow-prod-up_binary64_1869` `pow-plus_binary64_1862` `frac-add_binary64_1807`
3×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `unswap-sqr_binary64_1767` `*-commutative_binary64_1730`
2×	`pow2_binary64_1880` `pow-sqr_binary64_1772` `associate-+r+_binary64_1731`
1×	`+-commutative_binary64_1729` `distribute-lft-out_binary64_1750` `associate-+l+_binary64_1732`

Counts

4 → 95

Calls

4 calls:

27.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 a 4) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 b b) (.f64 (.f64 a a) (+.f64 a 1)))))
10.0ms	(.f64 (.f64 a a) (*.f64 b b))
10.0ms	(.f64 (.f64 a a) (+.f64 a 1))
8.0ms	(.f64 4 (+.f64 (.f64 b b) (.f64 (.f64 a a) (+.f64 a 1))))

series272.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 a a) (.f64 b b))) (+.f64 (pow.f64 a 4) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 b b) (.f64 (.f64 a a) (+.f64 a 1)))))
63.0ms	(.f64 (.f64 a a) (+.f64 a 1))
53.0ms	(.f64 4 (+.f64 (.f64 b b) (.f64 (.f64 a a) (+.f64 a 1))))
47.0ms	(.f64 (.f64 a a) (*.f64 b b))

simplify78.0ms (2%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5126	2770

prune206.0ms (5.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	107	3	110

Merged error: 0b

Counts

110 → 3

Compiler

Compiled 4808 to 2742 computations (43% saved)

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

rewrite49.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64_1860` `add-exp-log_binary64_1837`
13×	`add-log-exp_binary64_1838`
11×	`add-sqr-sqrt_binary64_1821` `add-cbrt-cube_binary64_1835`
10×	`*-un-lft-identity_binary64_1799`
8×	`add-cube-cbrt_binary64_1834` `associate-*r/_binary64_1741`
7×	`flip3-+_binary64_1802` `flip-+_binary64_1773` `associate-r_binary64_1739`
6×	`sum-log_binary64_1890`
5×	`prod-exp_binary64_1848` `pow-prod-down_binary64_1870`
4×	`associate-l_binary64_1740` `cbrt-unprod_binary64_1832` `frac-add_binary64_1807`
3×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `pow-unpow_binary64_1876`
2×	`unswap-sqr_binary64_1767` `associate-+r+_binary64_1731` `pow-exp_binary64_1867` `*-commutative_binary64_1730` `pow-pow_binary64_1871`
1×	`+-commutative_binary64_1729` `unpow2_binary64_1864` `pow-to-exp_binary64_1868` `unpow-prod-down_binary64_1878` `sqr-pow_binary64_1771` `distribute-lft-out_binary64_1750` `associate-+l+_binary64_1732`

Counts

4 → 84

Calls

4 calls:

17.0ms	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 a b) 2)) (+.f64 (pow.f64 a 4) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 b b) (.f64 (.f64 a a) (+.f64 a 1)))))
9.0ms	(.f64 (.f64 a a) (+.f64 a 1))
8.0ms	(.f64 4 (+.f64 (.f64 b b) (.f64 (.f64 a a) (+.f64 a 1))))
4.0ms	(pow.f64 (*.f64 a b) 2)

series275.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(+.f64 (+.f64 (.f64 2 (pow.f64 (.f64 a b) 2)) (+.f64 (pow.f64 a 4) (pow.f64 b 4))) (.f64 4 (+.f64 (.f64 b b) (.f64 (.f64 a a) (+.f64 a 1)))))
66.0ms	(.f64 (.f64 a a) (+.f64 a 1))
60.0ms	(.f64 4 (+.f64 (.f64 b b) (.f64 (.f64 a a) (+.f64 a 1))))
44.0ms	(pow.f64 (*.f64 a b) 2)

simplify74.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4987	2605
1	4987	2605

prune178.0ms (4.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	96	3	99

Merged error: 0b

Counts

99 → 3

Compiler

Compiled 3966 to 2494 computations (37.1% saved)

regimes78.0ms (2.1%)

Compiler: Compiled 675 to 484 computations (28.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	46
1	40	46

end0.0ms (0%)

sample834.0ms (21.8%)

Algorithm

1×

intervals

Results

547.0ms	8000×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 158 to 116 computations (26.6% saved)

Details

analyze144.0ms (3.8%)

sample25.0ms (0.6%)

simplify231.0ms (6%)

prune4.0ms (0.1%)

localize17.0ms (0.5%)

rewrite52.0ms (1.4%)

series260.0ms (6.8%)

simplify66.0ms (1.7%)

prune217.0ms (5.7%)

localize21.0ms (0.6%)

rewrite58.0ms (1.5%)

series253.0ms (6.6%)

simplify68.0ms (1.8%)

prune250.0ms (6.5%)

localize19.0ms (0.5%)

rewrite68.0ms (1.8%)

series272.0ms (7.1%)

simplify78.0ms (2%)

prune206.0ms (5.4%)

localize22.0ms (0.6%)

rewrite49.0ms (1.3%)

series275.0ms (7.2%)

simplify74.0ms (1.9%)

prune178.0ms (4.7%)

regimes78.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample834.0ms (21.8%)

Profiling