Details

analyze42.0ms

Algorithm

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

sample32.0ms

Algorithm

intervals

Results

14.0ms	86×	body	1280	valid
6.0ms	49×	body	640	valid
2.0ms	26×	body	320	valid
2.0ms	82×	body	80	valid
1.0ms	13×	body	160	valid
0.0ms	2×	body	80	invalid

simplify84.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4957	9
1	4957	9

prune1.0ms

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

Merged error: 30.4b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
3.6b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

2 → 25

Calls

2 calls:

2.0ms	(exp.f64 (*.f64 a x))
4.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

series42.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp.f64 (*.f64 a x))
28.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

simplify110.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4961	374
1	4961	374

prune33.0ms

Filtered

20 candidates to 31 candidates (-55.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	25	6	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	6	32

Merged error: 3.5b

Counts

32 → 6

localize12.0ms

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)))))))
3.8b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
5.8b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.4b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `prod-exp_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64`
4×	`associate-*r/_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64`
1×	`pow-to-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 74

Calls

4 calls:

5.0ms	(.f64 x (+.f64 a (.f64 x (+.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)))
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))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(.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)))
101.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
43.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify51.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5332	1832

prune85.0ms

Filtered

59 candidates to 86 candidates (-45.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 0.3b

Counts

92 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 x 1/6) a)
0.3b	(*.f64 x 1/6)
0.4b	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
9.7b	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64` `add-exp-log_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
9×	`log-prod_binary64`
6×	`associate-r_binary64` `unpow-prod-down_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `unpow-prod-up_binary64` `associate-l_binary64` `prod-exp_binary64`
3×	`rem-log-exp_binary64` `exp-prod_binary64`
2×	`pow-to-exp_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`pow-unpow_binary64` `log-pow_binary64` `unswap-sqr_binary64`

Counts

4 → 76

Calls

4 calls:

5.0ms	(.f64 (.f64 x 1/6) a)
4.0ms	(*.f64 x 1/6)
3.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
4.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

series204.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(.f64 (.f64 x 1/6) a)
11.0ms	(*.f64 x 1/6)
116.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
61.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

simplify63.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5337	1413

prune73.0ms

Filtered

57 candidates to 88 candidates (-54.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	88	8	96

Merged error: 0.3b

Counts

96 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/6)
1.4b	(.f64 x (+.f64 a (.f64 x (cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))) 3)))))
5.8b	(.f64 x (cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))) 3)))
18.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))) 3))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
18×	`cbrt-prod_binary64`
17×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64` `add-exp-log_binary64`
9×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`associate-*r/_binary64`
5×	`unswap-sqr_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `cube-div_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`unpow-prod-down_binary64` `cube-prod_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`rem-cbrt-cube_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 89

Calls

4 calls:

4.0ms	(*.f64 x 1/6)
5.0ms	(.f64 x (+.f64 a (.f64 x (cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))) 3)))))
7.0ms	(.f64 x (cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))) 3)))
4.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))) 3))

series223.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(*.f64 x 1/6)
90.0ms	(.f64 x (+.f64 a (.f64 x (cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))) 3)))))
78.0ms	(.f64 x (cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))) 3)))
42.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))) 3))

simplify60.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5745	2158

prune89.0ms

Filtered

75 candidates to 101 candidates (-34.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	101	8	109

Merged error: 0.3b

Counts

109 → 8

regimes191.0ms

Accuracy

87.1% (3.1b remaining)

Error of 3.4b against oracle of 0.2b and baseline of 24.6b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	100
1	51	100

end0.0ms

sample959.0ms

Algorithm

intervals

Results

500.0ms	2784×	body	1280	valid
150.0ms	1240×	body	640	valid
78.0ms	2811×	body	80	valid
60.0ms	753×	body	320	valid
22.0ms	412×	body	160	valid
4.0ms	152×	body	80	invalid

Details

analyze42.0ms

sample32.0ms

simplify84.0ms

prune1.0ms

localize5.0ms

rewrite6.0ms

series42.0ms

simplify110.0ms

prune33.0ms

localize12.0ms

rewrite31.0ms

series285.0ms

simplify51.0ms

prune85.0ms

localize13.0ms

rewrite19.0ms

series204.0ms

simplify63.0ms

prune73.0ms

localize15.0ms

rewrite23.0ms

series223.0ms

simplify60.0ms

prune89.0ms

regimes191.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample959.0ms

Profiling