Details

analyze218.0ms (4.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5024	18
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Symmetry

sort(a x)

Compiler

Compiled 7 to 7 computations (0% saved)

sample42.0ms (0.9%)

Algorithm

1×

intervals

Results

12.0ms	47×	body	2048	valid
9.0ms	63×	body	1024	valid
3.0ms	35×	body	512	valid
2.0ms	98×	body	128	valid
1.0ms	13×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4875	9
1	4875	9

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

30.2b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
3.4b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

30.1b

Rules

7×	`add-sqr-sqrt_binary64_1805`
6×	`add-log-exp_binary64_1822` `*-un-lft-identity_binary64_1783`
3×	`add-cube-cbrt_binary64_1818` `cancel-sign-sub-inv_binary64_1749`
2×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `difference-of-squares_binary64_1752`
1×	`diff-log_binary64_1875` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `difference-of-sqr-1_binary64_1753` `distribute-lft-out--_binary64_1735` `exp-to-pow_binary64_1845` `exp-prod_binary64_1835` `rem-exp-log_binary64_1823`

Counts

2 → 28

Calls

2 calls:

5.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(exp.f64 (*.f64 a x))

Compiler

Compiled 346 to 156 computations (54.9% saved)

series95.0ms (2.1%)

Error

0.3b

Counts

2 → 24

Calls

2 calls:

46.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
29.0ms	(exp.f64 (*.f64 a x))

Compiler

Compiled 648 to 510 computations (21.3% saved)

simplify60.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4917	652
1	4917	652

prune39.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	5	53

Error

0.4b

Counts

53 → 5

Compiler

Compiled 628 to 308 computations (51% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.4b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune5.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Error

0.4b

Counts

5 → 5

Compiler

Compiled 71 to 50 computations (29.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (*.f64 a x) 3)
1.2b	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
7.6b	(.f64 a (.f64 x x))
10.3b	(+.f64 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x))))) (.f64 1/6 (pow.f64 (.f64 a x) 3)))

rewrite113.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
11×	`add-sqr-sqrt_binary64_1805`
8×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`add-log-exp_binary64_1822` `associate-l_binary64_1724`
5×	`pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
4×	`associate-r_binary64_1723`
3×	`pow-unpow_binary64_1860`
2×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `distribute-rgt-in_binary64_1733` `associate-+l+_binary64_1716` `distribute-lft-in_binary64_1732` `unswap-sqr_binary64_1751` `-commutative_binary64_1714` `associate-r/_binary64_1725` `pow-pow_binary64_1855` `pow-exp_binary64_1851` `rem-cube-cbrt_binary64_1806`
1×	`sum-log_binary64_1874` `+-commutative_binary64_1713` `unpow-prod-down_binary64_1862` `pow-to-exp_binary64_1852` `unpow3_binary64_1849` `cube-mult_binary64_1813` `cube-prod_binary64_1811` `sqr-pow_binary64_1755`

Counts

4 → 76

Calls

4 calls:

8.0ms	(+.f64 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x))))) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
6.0ms	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
6.0ms	(.f64 a (.f64 x x))
4.0ms	(pow.f64 (*.f64 a x) 3)

Compiler

Compiled 2101 to 1026 computations (51.2% saved)

series663.0ms (14.8%)

Error

0.3b

Counts

4 → 42

Calls

4 calls:

307.0ms	(+.f64 (.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x))))) (.f64 1/6 (pow.f64 (.f64 a x) 3)))
170.0ms	(.f64 a (+.f64 x (.f64 1/2 (.f64 a (.f64 x x)))))
81.0ms	(pow.f64 (*.f64 a x) 3)
65.0ms	(.f64 a (.f64 x x))

Compiler

Compiled 1980 to 1485 computations (25% saved)

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5104	1721

prune119.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	119	4	123

Error

0.0b

Counts

123 → 4

Compiler

Compiled 2585 to 1318 computations (49% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a x) (.f64 (pow.f64 (.f64 a x) 2) (+.f64 1/2 (.f64 1/6 (*.f64 a x)))))
0.0b	(.f64 (pow.f64 (.f64 a x) 2) (+.f64 1/2 (.f64 1/6 (.f64 a x))))
0.3b	(pow.f64 (*.f64 a x) 2)
0.4b	(.f64 1/6 (.f64 a x))

rewrite111.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

20×	`add-exp-log_binary64_1821`
12×	`pow1_binary64_1844` `add-sqr-sqrt_binary64_1805`
11×	`add-cbrt-cube_binary64_1819`
9×	`prod-exp_binary64_1832` `associate-l_binary64_1724`
8×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`add-log-exp_binary64_1822`
4×	`pow-prod-down_binary64_1854` `cbrt-unprod_binary64_1816` `associate-r_binary64_1723` `pow-exp_binary64_1851`
3×	`pow-unpow_binary64_1860` `unpow2_binary64_1848` `sqr-pow_binary64_1755` `unswap-sqr_binary64_1751`
2×	`-commutative_binary64_1714` `unpow-prod-down_binary64_1862` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `flip3-+_binary64_1786` `associate-r/_binary64_1725` `flip-+_binary64_1757` `associate-+r+_binary64_1715`
1×	`sum-log_binary64_1874` `+-commutative_binary64_1713`

Counts

4 → 78

Calls

4 calls:

8.0ms	(.f64 (pow.f64 (.f64 a x) 2) (+.f64 1/2 (.f64 1/6 (.f64 a x))))
5.0ms	(.f64 1/6 (.f64 a x))
5.0ms	(+.f64 (.f64 a x) (.f64 (pow.f64 (.f64 a x) 2) (+.f64 1/2 (.f64 1/6 (*.f64 a x)))))
4.0ms	(pow.f64 (*.f64 a x) 2)

Compiler

Compiled 2017 to 1065 computations (47.2% saved)

series634.0ms (14.1%)

Error

0.0b

Counts

4 → 42

Calls

4 calls:

302.0ms	(+.f64 (.f64 a x) (.f64 (pow.f64 (.f64 a x) 2) (+.f64 1/2 (.f64 1/6 (*.f64 a x)))))
184.0ms	(.f64 (pow.f64 (.f64 a x) 2) (+.f64 1/2 (.f64 1/6 (.f64 a x))))
57.0ms	(pow.f64 (*.f64 a x) 2)
56.0ms	(.f64 1/6 (.f64 a x))

Compiler

Compiled 1920 to 1415 computations (26.3% saved)

simplify48.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5251	1923

prune107.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	120	4	124

Error

0.0b

Counts

124 → 4

Compiler

Compiled 2379 to 1209 computations (49.2% saved)

regimes341.0ms (7.6%)

Accuracy

Total 0.3b remaining (85.7%)

Threshold costs 0.3b (85.7%)

Compiler

Compiled 3306 to 2339 computations (29.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	65
1	40	65

Removed

((sort a x))

Compiler

Compiled 86 to 46 computations (46.5% saved)

end0.0ms (0%)

sample1.7s (37.4%)

Algorithm

1×

intervals

Results

409.0ms	1428×	body	2048	valid
235.0ms	1736×	body	1024	valid
86.0ms	1071×	body	512	valid
73.0ms	3103×	body	128	valid
35.0ms	662×	body	256	valid
3.0ms	140×	body	128	invalid

Compiler

Compiled 684 to 472 computations (31% saved)

Details

analyze218.0ms (4.9%)

sample42.0ms (0.9%)

simplify64.0ms (1.4%)

prune2.0ms (0%)

localize4.0ms (0.1%)

rewrite35.0ms (0.8%)

series95.0ms (2.1%)

simplify60.0ms (1.3%)

prune39.0ms (0.9%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize12.0ms (0.3%)

rewrite113.0ms (2.5%)

series663.0ms (14.8%)

simplify64.0ms (1.4%)

prune119.0ms (2.7%)

localize9.0ms (0.2%)

rewrite111.0ms (2.5%)

series634.0ms (14.1%)

simplify48.0ms (1.1%)

prune107.0ms (2.4%)

regimes341.0ms (7.6%)

bsearch1.0ms (0%)

simplify11.0ms (0.2%)

end0.0ms (0%)

sample1.7s (37.4%)

Profiling