Details

analyze224.0ms (3.9%)

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 (0.7%)

Algorithm

1×

intervals

Results

11.0ms	49×	body	2048	valid
8.0ms	59×	body	1024	valid
2.0ms	99×	body	128	valid
2.0ms	24×	body	512	valid
1.0ms	25×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

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

30.0b

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))
5.1b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

29.9b

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:

9.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(exp.f64 (*.f64 a x))

Compiler

Compiled 346 to 156 computations (54.9% saved)

series91.0ms (1.6%)

Error

0.3b

Counts

2 → 20

Calls

2 calls:

46.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
32.0ms	(exp.f64 (*.f64 a x))

Compiler

Compiled 528 to 422 computations (20.1% saved)

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4961	510
1	4961	510

prune35.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	6	49

Error

0.3b

Counts

49 → 6

Compiler

Compiled 516 to 259 computations (49.8% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.3b
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

6 alts after pruning (5 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	0	0
Total	6	6

Error

0.3b

Counts

6 → 6

Compiler

Compiled 59 to 50 computations (15.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
4.9b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
7.3b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
11.2b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite136.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

18×	`add-exp-log_binary64_1821`
13×	`add-cbrt-cube_binary64_1819` `add-sqr-sqrt_binary64_1805`
10×	`pow1_binary64_1844`
9×	`add-cube-cbrt_binary64_1818` `-un-lft-identity_binary64_1783` `prod-exp_binary64_1832` `associate-l*_binary64_1724`
7×	`associate-r_binary64_1723`
6×	`add-log-exp_binary64_1822`
5×	`cbrt-unprod_binary64_1816`
4×	`associate-*r/_binary64_1725`
3×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `pow-prod-down_binary64_1854` `*-commutative_binary64_1714`
2×	`unswap-sqr_binary64_1751` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732`
1×	`sum-log_binary64_1874` `+-commutative_binary64_1713` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 74

Calls

4 calls:

10.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
7.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
6.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))

Compiler

Compiled 2333 to 1422 computations (39% saved)

series815.0ms (14.3%)

Error

0.3b

Counts

4 → 48

Calls

4 calls:

313.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
202.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
169.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
90.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))

Compiler

Compiled 2060 to 1566 computations (24% saved)

simplify51.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5442	2357

prune124.0ms (2.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	120	8	128

Error

0.3b

Counts

128 → 8

Compiler

Compiled 2770 to 1621 computations (41.5% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

10.9b	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
10.9b	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 1/6 x) a))))))
10.9b	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 1/6 x) a))))))
11.2b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite361.0ms (6.3%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

9×	`cbrt-prod_binary64_1814`
7×	`add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
6×	`add-log-exp_binary64_1822` `cbrt-div_binary64_1815`
4×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `flip3-+_binary64_1786` `flip-+_binary64_1757`
3×	`pow1/3_binary64_1865`
1×	`sum-log_binary64_1874` `+-commutative_binary64_1713`

Counts

4 → 50

Calls

4 calls:

7.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
3.0ms	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 1/6 x) a))))))
3.0ms	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 1/6 x) a))))))
3.0ms	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))

Compiler

Compiled 3619 to 2193 computations (39.4% saved)

series704.0ms (12.3%)

Error

0.3b

Counts

4 → 42

Calls

4 calls:

181.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
149.0ms	(cbrt.f64 (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))))
148.0ms	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 1/6 x) a))))))
137.0ms	(cbrt.f64 (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 1/6 x) a))))))

Compiler

Compiled 6228 to 4376 computations (29.7% saved)

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4902	2488
1	4902	2488

prune240.0ms (4.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	93	7	100

Error

0.3b

Counts

100 → 7

Compiler

Compiled 5413 to 3317 computations (38.7% saved)

regimes522.0ms (9.1%)

Accuracy

Total 0.5b remaining (72.7%)

Threshold costs 0.5b (72.7%)

Compiler

Compiled 6241 to 4319 computations (30.8% saved)

bsearch4.0ms (0.1%)

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	27
1	25	27

Remove

(sort a x)

Compiler

Compiled 36 to 24 computations (33.3% saved)

end0.0ms (0%)

sample2.0s (35.3%)

Algorithm

1×

intervals

Results

418.0ms	1463×	body	2048	valid
252.0ms	1741×	body	1024	valid
96.0ms	1128×	body	512	valid
75.0ms	3033×	body	128	valid
32.0ms	635×	body	256	valid
3.0ms	131×	body	128	invalid

Compiler

Compiled 1244 to 855 computations (31.3% saved)

Details

analyze224.0ms (3.9%)

sample42.0ms (0.7%)

simplify65.0ms (1.1%)

prune2.0ms (0%)

localize4.0ms (0.1%)

rewrite37.0ms (0.6%)

series91.0ms (1.6%)

simplify94.0ms (1.6%)

prune35.0ms (0.6%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

rewrite136.0ms (2.4%)

series815.0ms (14.3%)

simplify51.0ms (0.9%)

prune124.0ms (2.2%)

localize26.0ms (0.5%)

rewrite361.0ms (6.3%)

series704.0ms (12.3%)

simplify86.0ms (1.5%)

prune240.0ms (4.2%)

regimes522.0ms (9.1%)

bsearch4.0ms (0.1%)

simplify10.0ms (0.2%)

end0.0ms (0%)

sample2.0s (35.3%)

Profiling