Details

analyze1.7s

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

sample1.6s

Algorithm

intervals

Results

1.5s	125×	body	5120	exit
75.0ms	256×	body	80	valid
6.0ms	384×	pre	80	true
1.0ms	3×	body	80	invalid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5925	119

prune32.0ms

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: 1.8b

Counts

2 → 2

localize89.0ms

Local error

Found 4 expressions with local error:

4.8b	(-.f64 (-.f64 1 z) 1)
4.8b	(-.f64 (-.f64 1 z) 1)
4.8b	(-.f64 (-.f64 1 z) 1)
4.8b	(-.f64 (-.f64 1 z) 1)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_574`
24×	`add-log-exp_binary64_539`
20×	`add-sqr-sqrt_binary64_559`
12×	`distribute-lft-out--_binary64_619` `diff-log_binary64_490`
8×	`sub-neg_binary64_578` `difference-of-squares_binary64_603`
4×	`flip3--_binary64_573` `add-cube-cbrt_binary64_545` `associate--l-_binary64_631` `pow1_binary64_520` `add-cbrt-cube_binary64_546` `associate--l+_binary64_630` `difference-of-sqr-1_binary64_604` `flip--_binary64_600` `add-exp-log_binary64_538`

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)

series35.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)

simplify130.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4867	660
1	4867	660

prune732.0ms

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: 1.8b

Counts

90 → 2

localize88.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
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))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64_574` `add-log-exp_binary64_539`
50×	`frac-add_binary64_564`
37×	`distribute-lft-out_binary64_618` `sum-log_binary64_489`
12×	`flip3-+_binary64_572` `flip-+_binary64_599`
7×	`pow1_binary64_520`
4×	`add-cube-cbrt_binary64_545` `add-cbrt-cube_binary64_546` `add-sqr-sqrt_binary64_559` `add-exp-log_binary64_538`
3×	`associate-+l+_binary64_626` `+-commutative_binary64_641`
2×	`sqrt-pow1_binary64_555`
1×	`sqrt-prod_binary64_553` `pow1/2_binary64_510` `pow-prod-down_binary64_501`

Counts

4 → 86

Calls

4 calls:

33.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
96.0ms	(+.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))
22.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

series85.0ms

Counts

4 → 10

Calls

4 calls:

24.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
44.0ms	(+.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))
16.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

simplify120.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5064	8305

prune968.0ms

Filtered

70 candidates to 96 candidates (-37.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	93	5	98

Merged error: 0.3b

Counts

98 → 5

localize142.0ms

Local error

Found 4 expressions with local error:

2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))
2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))
2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))
2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_574` `add-log-exp_binary64_539`
12×	`distribute-lft-out_binary64_618` `sum-log_binary64_489`
8×	`flip3-+_binary64_572` `flip-+_binary64_599` `frac-add_binary64_564`
4×	`add-cube-cbrt_binary64_545` `associate-+r+_binary64_625` `pow1_binary64_520` `add-cbrt-cube_binary64_546` `+-commutative_binary64_641` `add-sqr-sqrt_binary64_559` `add-exp-log_binary64_538`

Counts

4 → 68

Calls

4 calls:

25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))
26.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))
25.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))
28.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))

series60.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))
15.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))
15.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))
15.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 562949953421205/562949953421312))

simplify110.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4998	2240
1	4998	2240

prune2.9s

Filtered

60 candidates to 80 candidates (-33.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	80	5	85

Merged error: 0.3b

Counts

85 → 5

localize131.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 -3117477702829596018534405265335/2475880078570760549798248448 (/.f64 32953705673913248168464910359687/38685626227668133590597632 (-.f64 1 z)))
1.0b	(.f64 (.f64 (-.f64 2 z) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 848079078717083/1099511627776)
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.8b	(+.f64 (.f64 (-.f64 2 z) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z))))) (+.f64 -3117477702829596018534405265335/2475880078570760549798248448 (/.f64 32953705673913248168464910359687/38685626227668133590597632 (-.f64 1 z))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

18×	`flip3--_binary64_573` `flip--_binary64_600`
16×	`frac-add_binary64_564`
14×	`associate-*l/_binary64_636`
12×	`frac-times_binary64_566` `pow1_binary64_520`
11×	`add-log-exp_binary64_539`
10×	`flip3-+_binary64_572` `flip-+_binary64_599`
9×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
7×	`*-un-lft-identity_binary64_574`
6×	`associate-*r/_binary64_635`
5×	`add-cube-cbrt_binary64_545` `add-sqr-sqrt_binary64_559`
4×	`sum-log_binary64_489` `pow-prod-down_binary64_501`
3×	`cbrt-unprod_binary64_543` `associate-r_binary64_633` `prod-exp_binary64_525`
2×	`associate-+l+_binary64_626` `+-commutative_binary64_641` `sqrt-pow1_binary64_555` `sub-neg_binary64_578`
1×	`associate-+r+_binary64_625` `associate-l_binary64_634` `sqrt-prod_binary64_553` `distribute-lft-in_binary64_616` `pow1/2_binary64_510` `distribute-rgt-in_binary64_617` `distribute-lft-out_binary64_618` `*-commutative_binary64_642`

Counts

4 → 80

Calls

4 calls:

12.0ms	(+.f64 -3117477702829596018534405265335/2475880078570760549798248448 (/.f64 32953705673913248168464910359687/38685626227668133590597632 (-.f64 1 z)))
21.0ms	(.f64 (.f64 (-.f64 2 z) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 848079078717083/1099511627776)
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))
33.0ms	(+.f64 (.f64 (-.f64 2 z) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z))))) (+.f64 -3117477702829596018534405265335/2475880078570760549798248448 (/.f64 32953705673913248168464910359687/38685626227668133590597632 (-.f64 1 z))))

series53.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(+.f64 -3117477702829596018534405265335/2475880078570760549798248448 (/.f64 32953705673913248168464910359687/38685626227668133590597632 (-.f64 1 z)))
15.0ms	(.f64 (.f64 (-.f64 2 z) (-.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)))) 848079078717083/1099511627776)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
28.0ms	(+.f64 (.f64 (-.f64 2 z) (-.f64 316912650056936879084143652025/316912650057057350374175801344 (/.f64 35411260005907793929140321087001/77371252455336267181195264 (.f64 (-.f64 1 z) (-.f64 1 z))))) (+.f64 -3117477702829596018534405265335/2475880078570760549798248448 (/.f64 32953705673913248168464910359687/38685626227668133590597632 (-.f64 1 z))))

simplify123.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	6291	4027

prune1.9s

Filtered

76 candidates to 90 candidates (-18.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	88	7	95

Merged error: 0.3b

Counts

95 → 7

regimes634.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify59.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	1235	589
1	1235	589

end0.0ms

sample50.4s

Algorithm

intervals

Results

47.3s	3939×	body	5120	exit
2.5s	8000×	body	80	valid
205.0ms	12046×	pre	80	true
35.0ms	107×	body	80	invalid

Details

analyze1.7s

sample1.6s

simplify43.0ms

prune32.0ms

localize89.0ms

rewrite33.0ms

series35.0ms

simplify130.0ms

prune732.0ms

localize88.0ms

rewrite158.0ms

series85.0ms

simplify120.0ms

prune968.0ms

localize142.0ms

rewrite109.0ms

series60.0ms

simplify110.0ms

prune2.9s

localize131.0ms

rewrite72.0ms

series53.0ms

simplify123.0ms

prune1.9s

regimes634.0ms

bsearch0.0ms

simplify59.0ms

end0.0ms

sample50.4s

Profiling