Details

analyze152.0ms (0.6%)

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)

sample28.0ms (0.1%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify215.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4915	43
1	4915	43

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 58 to 38 computations (34.5% saved)

localize18.0ms (0.1%)

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))))
0.0b	(.f64 (.f64 a a) (-.f64 1 a))
0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.9b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite89.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1805`
18×	`associate-*r/_binary64_1725`
17×	`add-exp-log_binary64_1821` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
16×	`add-cbrt-cube_binary64_1819`
13×	`associate-r_binary64_1723`
12×	`add-cube-cbrt_binary64_1818`
7×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-prod-down_binary64_1854`
6×	`distribute-lft-in_binary64_1732` `cancel-sign-sub-inv_binary64_1749` `distribute-rgt-in_binary64_1733`
5×	`associate-l_binary64_1724`
4×	`frac-add_binary64_1791` `flip-+_binary64_1757` `flip3-+_binary64_1786` `add-log-exp_binary64_1822`
3×	`flip3--_binary64_1787` `pow-unpow_binary64_1860` `unpow-prod-down_binary64_1862` `*-commutative_binary64_1714` `unswap-sqr_binary64_1751` `flip--_binary64_1758`
2×	`difference-of-squares_binary64_1752` `sub-neg_binary64_1776`
1×	`sqr-pow_binary64_1755` `distribute-lft-out_binary64_1734` `unpow2_binary64_1848` `distribute-lft-out--_binary64_1735` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 100

Calls

4 calls:

25.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
19.0ms	(.f64 (.f64 a a) (-.f64 1 a))
16.0ms	(.f64 (.f64 b b) (+.f64 3 a))
9.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series213.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(.f64 (.f64 a a) (-.f64 1 a))
57.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
54.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
41.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify87.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4958	1932
1	4958	1932

prune777.0ms (3.2%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	84	28	112
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	29	113

Merged error: 0.0b

Counts

113 → 29

Compiler

Compiled 5165 to 2826 computations (45.3% saved)

localize20.0ms (0.1%)

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))))
0.0b	(.f64 (.f64 a a) (-.f64 1 a))
0.9b	(.f64 (.f64 b b) (+.f64 3 a))
1.4b	(.f64 (.f64 b b) (*.f64 a a))

rewrite76.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`pow1_binary64_1844`
28×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
21×	`pow-prod-down_binary64_1854`
18×	`associate-*r/_binary64_1725`
17×	`add-sqr-sqrt_binary64_1805`
15×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `*-un-lft-identity_binary64_1783`
14×	`associate-r_binary64_1723`
10×	`add-cube-cbrt_binary64_1818`
6×	`distribute-lft-in_binary64_1732` `cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `distribute-rgt-in_binary64_1733`
4×	`frac-add_binary64_1791` `flip-+_binary64_1757` `pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
3×	`flip3--_binary64_1787` `flip--_binary64_1758`
2×	`difference-of-squares_binary64_1752` `pow-sqr_binary64_1756` `sub-neg_binary64_1776` `pow2_binary64_1864`
1×	`distribute-lft-out_binary64_1734` `distribute-lft-out--_binary64_1735`

Counts

4 → 111

Calls

4 calls:

16.0ms	(.f64 (.f64 b b) (+.f64 3 a))
14.0ms	(.f64 (.f64 b b) (*.f64 a a))
14.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
10.0ms	(.f64 (.f64 a a) (-.f64 1 a))

series192.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))
42.0ms	(.f64 (.f64 a a) (-.f64 1 a))
42.0ms	(.f64 (.f64 b b) (+.f64 3 a))
30.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify86.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4968	1856
1	4968	1856

prune1.7s (6.8%)

Pruning

49 alts after pruning (47 fresh and 2 done)

	Pruned	Kept	Total
New	101	22	123
Fresh	2	25	27
Picked	0	1	1
Done	0	1	1
Total	103	49	152

Merged error: 0.0b

Counts

152 → 49

Compiler

Compiled 7454 to 4462 computations (40.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (*.f64 a a) (-.f64 1 a)) 4)
0.0b	(.f64 (.f64 a a) (-.f64 1 a))
0.2b	(.f64 (.f64 b b) 12)
1.4b	(.f64 (.f64 b b) (*.f64 a a))

rewrite61.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`pow1_binary64_1844`
35×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
26×	`pow-prod-down_binary64_1854`
20×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
14×	`add-sqr-sqrt_binary64_1805`
13×	`associate-r_binary64_1723`
12×	`*-un-lft-identity_binary64_1783`
9×	`add-cube-cbrt_binary64_1818`
6×	`cancel-sign-sub-inv_binary64_1749`
4×	`associate-r/_binary64_1725` `distribute-lft-in_binary64_1732` `pow-plus_binary64_1846` `pow-prod-up_binary64_1853` `associate-l_binary64_1724` `-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `add-log-exp_binary64_1822`
3×	`unswap-sqr_binary64_1751`
2×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `associate-*l/_binary64_1726` `pow-sqr_binary64_1756` `flip--_binary64_1758` `sub-neg_binary64_1776` `pow2_binary64_1864`
1×	`distribute-lft-out--_binary64_1735`

Counts

4 → 103

Calls

4 calls:

14.0ms	(.f64 (.f64 a a) (-.f64 1 a))
12.0ms	(.f64 (.f64 b b) (*.f64 a a))
12.0ms	(.f64 (.f64 (*.f64 a a) (-.f64 1 a)) 4)
11.0ms	(.f64 (.f64 b b) 12)

series125.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(.f64 (.f64 (*.f64 a a) (-.f64 1 a)) 4)
34.0ms	(.f64 (.f64 a a) (-.f64 1 a))
25.0ms	(.f64 (.f64 b b) (*.f64 a a))
23.0ms	(.f64 (.f64 b b) 12)

simplify86.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4977	1194
1	4977	1194

prune1.8s (7.5%)

Pruning

56 alts after pruning (53 fresh and 3 done)

	Pruned	Kept	Total
New	104	11	115
Fresh	4	42	46
Picked	0	1	1
Done	0	2	2
Total	108	56	164

Merged error: 0.0b

Counts

164 → 56

Compiler

Compiled 6892 to 4185 computations (39.3% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (*.f64 a a) (-.f64 1 a)) 4)
0.0b	(.f64 (.f64 a a) (-.f64 1 a))
0.1b	(pow.f64 (*.f64 b a) 2)
0.2b	(.f64 (.f64 b b) 12)

rewrite67.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-exp-log_binary64_1821` `pow1_binary64_1844`
23×	`add-cbrt-cube_binary64_1819`
15×	`add-sqr-sqrt_binary64_1805`
13×	`prod-exp_binary64_1832` `*-un-lft-identity_binary64_1783` `pow-prod-down_binary64_1854`
12×	`cbrt-unprod_binary64_1816` `associate-r_binary64_1723`
10×	`add-cube-cbrt_binary64_1818`
6×	`cancel-sign-sub-inv_binary64_1749`
4×	`associate-*r/_binary64_1725` `distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733` `add-log-exp_binary64_1822`
3×	`pow-unpow_binary64_1860` `associate-l_binary64_1724` `*-commutative_binary64_1714`
2×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `associate-*l/_binary64_1726` `pow-pow_binary64_1855` `unswap-sqr_binary64_1751` `flip--_binary64_1758` `sub-neg_binary64_1776` `pow-exp_binary64_1851`
1×	`sqr-pow_binary64_1755` `unpow2_binary64_1848` `unpow-prod-down_binary64_1862` `distribute-lft-out--_binary64_1735` `pow-to-exp_binary64_1852`

Counts

4 → 92

Calls

4 calls:

21.0ms	(.f64 (.f64 (*.f64 a a) (-.f64 1 a)) 4)
12.0ms	(.f64 (.f64 a a) (-.f64 1 a))
10.0ms	(.f64 (.f64 b b) 12)
5.0ms	(pow.f64 (*.f64 b a) 2)

series143.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(.f64 (.f64 (*.f64 a a) (-.f64 1 a)) 4)
39.0ms	(.f64 (.f64 a a) (-.f64 1 a))
32.0ms	(pow.f64 (*.f64 b a) 2)
22.0ms	(.f64 (.f64 b b) 12)

simplify101.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5052	1095

prune1.6s (6.8%)

Pruning

57 alts after pruning (53 fresh and 4 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	5	47	52
Picked	0	1	1
Done	0	3	3
Total	103	57	160

Merged error: 0.0b

Counts

160 → 57

Compiler

Compiled 3745 to 2442 computations (34.8% saved)

regimes4.6s (18.9%)

Compiler: Compiled 52724 to 36812 computations (30.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	52
1	54	52

end0.0ms (0%)

sample12.0s (49.4%)

Algorithm

1×

intervals

Results

658.0ms	8000×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 10082 to 7062 computations (30% saved)

Pareto

Details

analyze152.0ms (0.6%)

sample28.0ms (0.1%)

simplify215.0ms (0.9%)

prune3.0ms (0%)

localize18.0ms (0.1%)

rewrite89.0ms (0.4%)

series213.0ms (0.9%)

simplify87.0ms (0.4%)

prune777.0ms (3.2%)

localize20.0ms (0.1%)

rewrite76.0ms (0.3%)

series192.0ms (0.8%)

simplify86.0ms (0.4%)

prune1.7s (6.8%)

localize20.0ms (0.1%)

rewrite61.0ms (0.3%)

series125.0ms (0.5%)

simplify86.0ms (0.4%)

prune1.8s (7.5%)

localize30.0ms (0.1%)

rewrite67.0ms (0.3%)

series143.0ms (0.6%)

simplify101.0ms (0.4%)

prune1.6s (6.8%)

regimes4.6s (18.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample12.0s (49.4%)

Profiling