Details

analyze41.0ms

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

sample36.0ms

Algorithm

intervals

Results

18.0ms	79×	body	1280	valid
5.0ms	41×	body	640	valid
2.0ms	32×	body	320	valid
2.0ms	90×	body	80	valid
1.0ms	14×	body	160	valid
0.0ms	1×	body	80	invalid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4934	6
1	4934	6

prune3.0ms

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: 31.6b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
4.7b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite7.0ms

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))
5.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

series13.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(exp.f64 (*.f64 a x))
8.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)

simplify56.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4937	243
1	4937	243

prune41.0ms

Filtered

20 candidates to 31 candidates (-55.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	4	32

Merged error: 5.3b

Counts

32 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/6 (pow.f64 a 3))
5.8b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
8.6b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
8.6b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
13×	`add-cbrt-cube_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
9×	`associate-l_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64` `unswap-sqr_binary64`
4×	`unpow-prod-down_binary64` `cube-prod_binary64`
3×	`*-commutative_binary64`
2×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 83

Calls

4 calls:

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

series54.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 1/6 (pow.f64 a 3))
12.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
9.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
27.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4946	953
1	4946	953

prune89.0ms

Filtered

59 candidates to 95 candidates (-61.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	95	4	99

Merged error: 0.1b

Counts

99 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.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)
9.2b	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`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` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `exp-prod_binary64`
2×	`pow-to-exp_binary64` `associate-r/_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `pow-exp_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `pow-unpow_binary64` `log-pow_binary64` `flip-+_binary64`

Counts

4 → 81

Calls

4 calls:

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

series62.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))))
9.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
2.0ms	(*.f64 x 1/6)
18.0ms	(pow.f64 (exp.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))))

simplify56.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4972	1144
1	4972	1144

prune88.0ms

Filtered

62 candidates to 93 candidates (-50.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	93	4	97

Merged error: 0.1b

Counts

97 → 4

localize10.0ms

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)
8.6b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`associate-r_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-l_binary64`
6×	`associate-*r/_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `unswap-sqr_binary64` `flip-+_binary64`

Counts

4 → 86

Calls

4 calls:

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

series32.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (.f64 x 1/6) a)
8.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a)))
2.0ms	(*.f64 x 1/6)
18.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))))

simplify44.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5123	951

prune68.0ms

Filtered

57 candidates to 98 candidates (-71.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	98	4	102

Merged error: 0.1b

Counts

102 → 4

regimes260.0ms

Accuracy

87.3% (3.1b remaining)

Error of 3.4b against oracle of 0.3b and baseline of 24.7b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	77
1	62	77

end0.0ms

sample932.0ms

Algorithm

intervals

Results

468.0ms	2643×	body	1280	valid
154.0ms	1335×	body	640	valid
74.0ms	2842×	body	80	valid
62.0ms	767×	body	320	valid
22.0ms	413×	body	160	valid
3.0ms	128×	body	80	invalid

Details

analyze41.0ms

sample36.0ms

simplify38.0ms

prune3.0ms

localize4.0ms

rewrite7.0ms

series13.0ms

simplify56.0ms

prune41.0ms

localize12.0ms

rewrite33.0ms

series54.0ms

simplify56.0ms

prune89.0ms

localize13.0ms

rewrite22.0ms

series62.0ms

simplify56.0ms

prune88.0ms

localize10.0ms

rewrite30.0ms

series32.0ms

simplify44.0ms

prune68.0ms

regimes260.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample932.0ms

Profiling