Details

analyze44.0ms (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
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

Compiler

Compiled 7 to 7 computations (0% saved)

sample37.0ms (1.1%)

Algorithm

1×

intervals

Results

16.0ms	54×	body	2048	valid
8.0ms	55×	body	1024	valid
3.0ms	38×	body	512	valid
2.0ms	91×	body	128	valid
1.0ms	18×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify153.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4875	9
1	4875	9

prune2.0ms (0.1%)

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

30.5b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

3.6b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1123`
5×	`*-un-lft-identity_binary64_1101`
3×	`add-log-exp_binary64_1140` `cancel-sign-sub-inv_binary64_1067`
2×	`difference-of-squares_binary64_1070` `add-cube-cbrt_binary64_1136`
1×	`diff-log_binary64_1193` `add-exp-log_binary64_1139` `pow1_binary64_1162` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137`

Counts

1 → 18

Calls

1 calls:

5.0ms

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

series29.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

29.0ms

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

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4929	280
1	4929	280

prune26.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	17	4	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	4	22

Error

3.2b

Counts

22 → 4

Compiler

Compiled 297 to 156 computations (47.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.4b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
4.6b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
5.6b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
9.1b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite40.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_1139`
13×	`add-sqr-sqrt_binary64_1123` `add-cbrt-cube_binary64_1137`
10×	`pow1_binary64_1162`
9×	`-un-lft-identity_binary64_1101` `prod-exp_binary64_1150` `add-cube-cbrt_binary64_1136` `associate-l*_binary64_1042`
7×	`associate-r_binary64_1041`
6×	`add-log-exp_binary64_1140`
5×	`cbrt-unprod_binary64_1134`
4×	`associate-*r/_binary64_1043`
3×	`*-commutative_binary64_1032` `flip3-+_binary64_1104` `pow-prod-down_binary64_1172` `flip-+_binary64_1075`
2×	`distribute-lft-in_binary64_1050` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051`
1×	`pow-exp_binary64_1169` `sum-log_binary64_1192` `+-commutative_binary64_1031` `pow-to-exp_binary64_1170`

Counts

4 → 74

Calls

4 calls:

13.0ms	(.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)))))))

series253.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
82.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
47.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
40.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify45.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5442	1832

prune104.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	84	6	90

Error

0.2b

Counts

90 → 6

Compiler

Compiled 2290 to 1360 computations (40.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
0.3b	(*.f64 x 1/6)
1.4b	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
5.6b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite40.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
15×	`add-sqr-sqrt_binary64_1123`
11×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
10×	`-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136` `associate-r_binary64_1041` `associate-l*_binary64_1042`
8×	`associate-*r/_binary64_1043`
6×	`distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
4×	`*-commutative_binary64_1032` `add-log-exp_binary64_1140`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `unswap-sqr_binary64_1069`

Counts

4 → 90

Calls

4 calls:

13.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
8.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
6.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
4.0ms	(*.f64 x 1/6)

series196.0ms (6%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))))
70.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
33.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
10.0ms	(*.f64 x 1/6)

simplify48.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	6204	1933

prune102.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	102	6	108

Error

0.2b

Counts

108 → 6

Compiler

Compiled 2441 to 1417 computations (42% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
0.3b	(*.f64 x 1/6)
3.9b	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
5.6b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite48.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
20×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
17×	`distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
12×	`add-sqr-sqrt_binary64_1123` `associate-*r/_binary64_1043`
10×	`associate-l_binary64_1042`
9×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
8×	`associate-r_binary64_1041`
4×	`*-commutative_binary64_1032` `add-log-exp_binary64_1140`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`unswap-sqr_binary64_1069`

Counts

4 → 102

Calls

4 calls:

13.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
11.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
10.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
4.0ms	(*.f64 x 1/6)

series188.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
68.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
41.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
10.0ms	(*.f64 x 1/6)

simplify47.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5499	2104

prune108.0ms (3.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	114	6	120

Error

0.2b

Counts

120 → 6

Compiler

Compiled 2701 to 1439 computations (46.7% saved)

regimes255.0ms (7.8%)

Accuracy

Total 2.8b remaining (91.3%)

Threshold costs 0b (0%)

Compiler

Compiled 1752 to 1313 computations (25.1% saved)

bsearch1.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	48
1	42	48

end0.0ms (0%)

sample1.4s (42.5%)

Algorithm

1×

intervals

Results

409.0ms	1419×	body	2048	valid
266.0ms	1786×	body	1024	valid
93.0ms	1084×	body	512	valid
85.0ms	3099×	body	128	valid
35.0ms	612×	body	256	valid
4.0ms	132×	body	128	invalid

Compiler

Compiled 357 to 260 computations (27.2% saved)

Details

analyze44.0ms (1.4%)

sample37.0ms (1.1%)

simplify153.0ms (4.7%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite6.0ms (0.2%)

series29.0ms (0.9%)

simplify67.0ms (2%)

prune26.0ms (0.8%)

localize12.0ms (0.4%)

rewrite40.0ms (1.2%)

series253.0ms (7.7%)

simplify45.0ms (1.4%)

prune104.0ms (3.2%)

localize11.0ms (0.3%)

rewrite40.0ms (1.2%)

series196.0ms (6%)

simplify48.0ms (1.5%)

prune102.0ms (3.1%)

localize11.0ms (0.3%)

rewrite48.0ms (1.5%)

series188.0ms (5.7%)

simplify47.0ms (1.4%)

prune108.0ms (3.3%)

regimes255.0ms (7.8%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (42.5%)

Profiling