Details

analyze209.0ms (6.2%)

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

Compiler

Compiled 7 to 7 computations (0% saved)

sample38.0ms (1.1%)

Algorithm

1×

intervals

Results

15.0ms	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)

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4875	9
1	4875	9

prune2.0ms (0.1%)

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)

rewrite5.0ms (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:

4.0ms

(-.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

prune25.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	3	22

Error

4.7b

Counts

22 → 3

Compiler

Compiled 268 to 139 computations (48.1% 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)))))))
5.0b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
5.1b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
9.9b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite36.0ms (1.1%)

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:

10.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.0ms	(.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))))
5.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))

series261.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
87.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
43.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
42.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify46.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5442	1832

prune100.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Error

0.2b

Counts

89 → 5

Compiler

Compiled 2255 to 1338 computations (40.7% saved)

localize12.0ms (0.4%)

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)
3.3b	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
5.1b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite45.0ms (1.3%)

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:

12.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
12.0ms	(.f64 x (.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)))
4.0ms	(*.f64 x 1/6)

series195.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
73.0ms	(.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)

simplify47.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5499	2104

prune111.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	114	5	119

Error

0.2b

Counts

119 → 5

Compiler

Compiled 2768 to 1491 computations (46.1% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 x 1/6) a)
0.3b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
0.3b	(*.f64 x 1/6)
6.6b	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`pow1_binary64_1162`
16×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
13×	`add-sqr-sqrt_binary64_1123`
10×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`associate-r_binary64_1041`
7×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
5×	`associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140` `pow-pow_binary64_1173`
3×	`*-commutative_binary64_1032` `unpow-prod-down_binary64_1180` `exp-prod_binary64_1153`
2×	`unpow-prod-up_binary64_1179` `distribute-lft-in_binary64_1050` `associate-*r/_binary64_1043` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051`
1×	`pow-exp_binary64_1169` `flip3-+_binary64_1104` `pow-unpow_binary64_1178` `flip-+_binary64_1075` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170`

Counts

4 → 79

Calls

4 calls:

8.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
7.0ms	(.f64 (.f64 x 1/6) a)
4.0ms	(*.f64 x 1/6)
4.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

series118.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow.f64 (exp.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)))
14.0ms	(.f64 (.f64 x 1/6) a)
11.0ms	(*.f64 x 1/6)

simplify75.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5128	1372

prune92.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	91	5	96

Error

0.2b

Counts

96 → 5

Compiler

Compiled 2140 to 1212 computations (43.4% saved)

regimes263.0ms (7.9%)

Accuracy

Total 2.9b remaining (91.8%)

Threshold costs 0b (0%)

Compiler

Compiled 1567 to 1193 computations (23.9% saved)

bsearch1.0ms (0%)

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

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	51
1	42	51

Compiler

Compiled 68 to 44 computations (35.3% saved)

end0.0ms (0%)

sample1.4s (43.2%)

Algorithm

1×

intervals

Results

421.0ms	1419×	body	2048	valid
268.0ms	1786×	body	1024	valid
97.0ms	1084×	body	512	valid
90.0ms	3099×	body	128	valid
34.0ms	612×	body	256	valid
4.0ms	132×	body	128	invalid

Compiler

Compiled 322 to 236 computations (26.7% saved)

Details

analyze209.0ms (6.2%)

sample38.0ms (1.1%)

simplify64.0ms (1.9%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite5.0ms (0.2%)

series29.0ms (0.9%)

simplify67.0ms (2%)

prune25.0ms (0.7%)

localize12.0ms (0.4%)

rewrite36.0ms (1.1%)

series261.0ms (7.8%)

simplify46.0ms (1.4%)

prune100.0ms (3%)

localize12.0ms (0.4%)

rewrite45.0ms (1.3%)

series195.0ms (5.8%)

simplify47.0ms (1.4%)

prune111.0ms (3.3%)

localize12.0ms (0.4%)

rewrite29.0ms (0.9%)

series118.0ms (3.5%)

simplify75.0ms (2.2%)

prune92.0ms (2.8%)

regimes263.0ms (7.9%)

bsearch1.0ms (0%)

simplify9.0ms (0.3%)

end0.0ms (0%)

sample1.4s (43.2%)

Profiling