Details

analyze47.0ms (0.9%)

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)

sample66.0ms (1.3%)

Algorithm

1×

intervals

Results

24.0ms	49×	body	2048	valid
17.0ms	65×	body	1024	valid
5.0ms	31×	body	512	valid
4.0ms	83×	body	128	valid
3.0ms	28×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify216.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4875	9
1	4875	9

prune3.0ms (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

32.6b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

4.9b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_441`
5×	`*-un-lft-identity_binary64_419`
3×	`add-log-exp_binary64_458` `cancel-sign-sub-inv_binary64_385`
2×	`difference-of-squares_binary64_388` `add-cube-cbrt_binary64_454`
1×	`sub-neg_binary64_412` `difference-of-sqr-1_binary64_389` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `diff-log_binary64_511` `flip--_binary64_394` `pow1_binary64_480`

Counts

1 → 18

Calls

1 calls:

7.0ms

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

series30.0ms (0.6%)

Counts

1 → 3

Calls

1 calls:

30.0ms

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

simplify104.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4929	280
1	4929	280

prune42.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	4	22

Error

5.3b

Counts

22 → 4

Compiler

Compiled 288 to 147 computations (49% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
6.2b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
6.4b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
8.2b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite56.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_457`
13×	`add-sqr-sqrt_binary64_441` `add-cbrt-cube_binary64_455`
10×	`pow1_binary64_480`
9×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `associate-l*_binary64_360`
7×	`associate-r_binary64_359`
6×	`add-log-exp_binary64_458`
5×	`cbrt-unprod_binary64_452`
4×	`associate-*r/_binary64_361`
3×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `*-commutative_binary64_350` `flip-+_binary64_393`
2×	`distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `distribute-lft-in_binary64_368`
1×	`pow-exp_binary64_487` `sum-log_binary64_510` `pow-to-exp_binary64_488` `+-commutative_binary64_349`

Counts

4 → 74

Calls

4 calls:

18.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
10.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
10.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
8.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

series665.0ms (13.3%)

Counts

4 → 12

Calls

4 calls:

420.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
119.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
76.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
49.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify59.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5442	1832

prune144.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	82	8	90

Error

0.1b

Counts

90 → 8

Compiler

Compiled 2294 to 1362 computations (40.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
0.4b	(*.f64 x 1/6)
2.9b	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
6.2b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite61.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
20×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
17×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
12×	`add-sqr-sqrt_binary64_441` `associate-*r/_binary64_361`
10×	`associate-l_binary64_360`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`associate-r_binary64_359`
4×	`add-log-exp_binary64_458` `*-commutative_binary64_350`
3×	`flip3-+_binary64_422` `flip-+_binary64_393`
2×	`unswap-sqr_binary64_387`

Counts

4 → 102

Calls

4 calls:

24.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
16.0ms	(.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)))
4.0ms	(*.f64 x 1/6)

series264.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(.f64 x (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
101.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))
34.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
10.0ms	(*.f64 x 1/6)

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5499	2104

prune155.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	114	8	122

Error

0.1b

Counts

122 → 8

Compiler

Compiled 2807 to 1515 computations (46% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 x 1/6) a)
0.2b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
0.4b	(*.f64 x 1/6)
8.3b	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

rewrite52.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`pow1_binary64_480`
16×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
13×	`add-sqr-sqrt_binary64_441`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`associate-r_binary64_359`
7×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
5×	`associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `pow-pow_binary64_491`
3×	`unpow-prod-down_binary64_498` `exp-prod_binary64_471` `*-commutative_binary64_350`
2×	`distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `unpow-prod-up_binary64_497` `associate-*r/_binary64_361` `distribute-lft-in_binary64_368`
1×	`flip3-+_binary64_422` `pow-exp_binary64_487` `sqr-pow_binary64_391` `pow-to-exp_binary64_488` `flip-+_binary64_393` `pow-unpow_binary64_496`

Counts

4 → 79

Calls

4 calls:

16.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
10.0ms	(.f64 (.f64 x 1/6) a)
8.0ms	(*.f64 x 1/6)
5.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

series180.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))
46.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
25.0ms	(.f64 (.f64 x 1/6) a)
17.0ms	(*.f64 x 1/6)

simplify127.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5128	1372

prune152.0ms (3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	91	8	99

Error

0.1b

Counts

99 → 8

Compiler

Compiled 2140 to 1212 computations (43.4% saved)

regimes370.0ms (7.4%)

Accuracy

Total 3.1b remaining (93.3%)

Threshold costs 0b (0%)

Compiler

Compiled 1431 to 1057 computations (26.1% 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	50	72
1	50	72

end0.0ms (0%)

sample2.1s (41.4%)

Algorithm

1×

intervals

Results

628.0ms	1443×	body	2048	valid
390.0ms	1741×	body	1024	valid
143.0ms	1090×	body	512	valid
117.0ms	3072×	body	128	valid
52.0ms	654×	body	256	valid
5.0ms	135×	body	128	invalid

Compiler

Compiled 318 to 226 computations (28.9% saved)

Details

analyze47.0ms (0.9%)

sample66.0ms (1.3%)

simplify216.0ms (4.3%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite9.0ms (0.2%)

series30.0ms (0.6%)

simplify104.0ms (2.1%)

prune42.0ms (0.8%)

localize12.0ms (0.2%)

rewrite56.0ms (1.1%)

series665.0ms (13.3%)

simplify59.0ms (1.2%)

prune144.0ms (2.9%)

localize12.0ms (0.2%)

rewrite61.0ms (1.2%)

series264.0ms (5.3%)

simplify87.0ms (1.7%)

prune155.0ms (3.1%)

localize12.0ms (0.2%)

rewrite52.0ms (1%)

series180.0ms (3.6%)

simplify127.0ms (2.5%)

prune152.0ms (3%)

regimes370.0ms (7.4%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.1s (41.4%)

Profiling