Details

analyze1.9s

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

sample1.7s

Algorithm

intervals

Results

1.6s	137×	body	5120	exit
75.0ms	256×	body	80	valid
6.0ms	397×	pre	80	true
1.0ms	4×	body	80	invalid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4652	74
1	4652	74

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 2.1b

Counts

2 → 2

localize61.0ms

Local error

Found 4 expressions with local error:

5.5b	(-.f64 (-.f64 1 z) 1)
5.5b	(-.f64 (-.f64 1 z) 1)
5.5b	(-.f64 (-.f64 1 z) 1)
5.5b	(-.f64 (-.f64 1 z) 1)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
24×	`add-log-exp_binary64`
20×	`add-sqr-sqrt_binary64`
12×	`diff-log_binary64` `distribute-lft-out--_binary64`
8×	`sub-neg_binary64` `difference-of-squares_binary64`
4×	`pow1_binary64` `flip3--_binary64` `associate--l-_binary64` `add-cube-cbrt_binary64` `difference-of-sqr-1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 76

Calls

4 calls:

8.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)

series8.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(-.f64 (-.f64 1 z) 1)
2.0ms	(-.f64 (-.f64 1 z) 1)

simplify65.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5347	436

prune406.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	88	2	90

Merged error: 2.1b

Counts

90 → 2

localize57.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
1.2b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.5b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
44×	`add-log-exp_binary64` `frac-add_binary64`
31×	`distribute-lft-out_binary64` `sum-log_binary64`
10×	`add-exp-log_binary64`
9×	`flip3-+_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
7×	`prod-exp_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`
2×	`pow-prod-down_binary64` `associate-+l+_binary64` `sqrt-pow1_binary64` `+-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `associate-r/_binary64` `associate-l_binary64` `pow-sub_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

92.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
16.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
22.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

series44.0ms

Counts

4 → 10

Calls

4 calls:

14.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
25.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
5.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

simplify63.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5036	5320

prune514.0ms

Filtered

69 candidates to 96 candidates (-39.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	91	7	98

Merged error: 0.3b

Counts

98 → 7

localize102.0ms

Local error

Found 4 expressions with local error:

2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
12×	`distribute-lft-out_binary64` `sum-log_binary64`
8×	`flip3-+_binary64` `frac-add_binary64` `flip-+_binary64`
4×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `associate-+r+_binary64`

Counts

4 → 68

Calls

4 calls:

23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series19.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
5.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
4.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
5.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

simplify62.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5149	1488

prune2.8s

Filtered

60 candidates to 80 candidates (-33.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	80	7	87

Merged error: 0.3b

Counts

87 → 7

localize128.0ms

Local error

Found 4 expressions with local error:

2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.5b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.6b	(+.f64 (+.f64 -1754983927599566241463270563990074949040428675/1393796574908163946345982392040522594123776 (/.f64 -32953705673913248168464910359687/38685626227668133590597632 (/.f64 (-.f64 1 z) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)))) (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-log-exp_binary64`
22×	`frac-add_binary64`
21×	`flip3-+_binary64` `flip-+_binary64`
19×	`*-un-lft-identity_binary64`
12×	`sum-log_binary64`
9×	`distribute-lft-out_binary64`
8×	`frac-times_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`associate-+r+_binary64`
4×	`pow1_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `associate-l/_binary64`
1×	`associate-+l+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 82

Calls

4 calls:

23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
23.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
51.0ms	(+.f64 (+.f64 -1754983927599566241463270563990074949040428675/1393796574908163946345982392040522594123776 (/.f64 -32953705673913248168464910359687/38685626227668133590597632 (/.f64 (-.f64 1 z) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)))) (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))))

series28.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
5.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
8.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
11.0ms	(+.f64 (+.f64 -1754983927599566241463270563990074949040428675/1393796574908163946345982392040522594123776 (/.f64 -32953705673913248168464910359687/38685626227668133590597632 (/.f64 (-.f64 1 z) (-.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312)))) (*.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))))

simplify90.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5636	3566

prune5.3s

Filtered

79 candidates to 94 candidates (-19.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	94	7	101

Merged error: 0.3b

Counts

101 → 7

regimes172.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	243	424
1	243	424

end0.0ms

sample48.7s

Algorithm

intervals

Results

45.6s	3799×	body	5120	exit
2.5s	8000×	body	80	valid
216.0ms	11889×	pre	80	true
30.0ms	90×	body	80	invalid

Details

analyze1.9s

sample1.7s

simplify42.0ms

prune13.0ms

localize61.0ms

rewrite34.0ms

series8.0ms

simplify65.0ms

prune406.0ms

localize57.0ms

rewrite136.0ms

series44.0ms

simplify63.0ms

prune514.0ms

localize102.0ms

rewrite96.0ms

series19.0ms

simplify62.0ms

prune2.8s

localize128.0ms

rewrite126.0ms

series28.0ms

simplify90.0ms

prune5.3s

regimes172.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample48.7s

Profiling