Details

analyze730.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

sample64.0ms

Algorithm

intervals

Results

12.0ms	176×	body	80	valid
9.0ms	27×	body	1280	valid
7.0ms	22×	body	1280	nan
6.0ms	23×	body	640	valid
5.0ms	45×	body	80	nan
4.0ms	18×	body	640	nan
4.0ms	20×	body	320	valid
2.0ms	9×	body	320	nan
1.0ms	10×	body	160	valid
0.0ms	4×	body	160	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5288	27

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: 41.6b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
12.0b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.0b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 79

Calls

4 calls:

17.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
15.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
13.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms	(* (sqrt 2.0) t)
57.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
189.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify47.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5001	2021

prune218.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 4.6b

Counts

93 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
0.8b	(+ (* t t) (* l (/ l x)))
3.4b	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
28.1b	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-*r/`
8×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
7×	`pow1` `sqrt-prod`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`associate-r`
2×	`+-commutative` `associate-+r+` `sum-log` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 65

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
4.0ms	(+ (* t t) (* l (/ l x)))
8.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
8.0ms	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sqrt 2.0) t)
9.0ms	(+ (* t t) (* l (/ l x)))
15.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
24.0ms	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

simplify29.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5237	1359

prune183.0ms

Filtered

58 candidates to 77 candidates (-32.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	72	10	82

Merged error: 4.5b

Counts

82 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
0.8b	(+ (* t t) (* l (/ l x)))
3.4b	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
28.1b	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
16×	`add-exp-log`
12×	`associate-*r/`
10×	`add-cbrt-cube`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`sqrt-prod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `*-commutative`

Counts

4 → 65

Calls

4 calls:

11.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
4.0ms	(+ (* t t) (* l (/ l x)))
10.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
8.0ms	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
9.0ms	(+ (* t t) (* l (/ l x)))
15.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
25.0ms	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

simplify32.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5452	1355

prune211.0ms

Filtered

52 candidates to 77 candidates (-48.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	76	11	87

Merged error: 4.5b

Counts

87 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
0.8b	(+ (* t t) (* l (/ l x)))
3.4b	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
28.1b	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-*r/` `sqrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-sqr-sqrt` `associate-l` `add-cbrt-cube`
8×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`sqrt-div` `frac-add`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 67

Calls

4 calls:

9.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
4.0ms	(+ (* t t) (* l (/ l x)))
8.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
8.0ms	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
9.0ms	(+ (* t t) (* l (/ l x)))
14.0ms	(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
24.0ms	(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

simplify175.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5324	1384

prune163.0ms

Filtered

57 candidates to 79 candidates (-38.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	78	12	90

Merged error: 4.5b

Counts

90 → 12

regimes567.0ms

Accuracy

76.1% (5.8b remaining)

Error of 9.7b against oracle of 3.9b and baseline of 28.0b

bsearch405.0ms

Steps

Iters	Range		Point
9	1.5534399410893068e+38	1.1219144275365117e+45	1.106062725366667e+45
11	7.192105036690047e-175	2.1633163245864085e-153	7.28019137526069e-175
8	2.3986175275417474e-287	1.5585890522253495e-283	1.5320629240773466e-283
9	-1.1119318115074067e+108	-7.679526239006972e+99	-1.0963713958029977e+108

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	300	153
1	300	153

end0.0ms

sample1.8s

Algorithm

intervals

Results

370.0ms	5174×	body	80	valid
273.0ms	842×	body	1280	valid
249.0ms	991×	body	640	valid
160.0ms	517×	body	1280	nan
155.0ms	615×	body	640	nan
126.0ms	641×	body	320	valid
88.0ms	1380×	body	80	nan
54.0ms	298×	body	320	nan
48.0ms	352×	body	160	valid
23.0ms	185×	body	160	nan

Details

analyze730.0ms

sample64.0ms

simplify34.0ms

prune13.0ms

localize15.0ms

rewrite52.0ms

series340.0ms

simplify47.0ms

prune218.0ms

localize18.0ms

rewrite27.0ms

series55.0ms

simplify29.0ms

prune183.0ms

localize18.0ms

rewrite35.0ms

series53.0ms

simplify32.0ms

prune211.0ms

localize20.0ms

rewrite31.0ms

series51.0ms

simplify175.0ms

prune163.0ms

regimes567.0ms

bsearch405.0ms

simplify4.0ms

end0.0ms

sample1.8s

Profiling