Details

analyze782.0ms

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

sample63.0ms

Algorithm

intervals

Results

11.0ms	159×	body	80	valid
10.0ms	37×	body	640	valid
7.0ms	24×	body	320	valid
6.0ms	17×	body	1280	nan
5.0ms	16×	body	1280	valid
4.0ms	16×	body	640	nan
3.0ms	42×	body	80	nan
3.0ms	20×	body	160	valid
1.0ms	8×	body	160	nan
1.0ms	4×	body	320	nan

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5225	27

prune11.0ms

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: 42.0b

Counts

2 → 2

localize16.0ms

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)
15.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite53.0ms

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))))
7.0ms	(* (sqrt 2.0) t)
13.0ms	(- (* (/ (+ 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)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (* (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)
58.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
188.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify45.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5044	2021

prune216.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 3.2b

Counts

93 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
1.0b	(+ (* t t) (/ l (/ x l)))
4.4b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
24.9b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `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)
11.0ms	(+ (* t t) (/ l (/ x l)))
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
11.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify29.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5246	1361

prune171.0ms

Filtered

61 candidates to 77 candidates (-26.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	72	11	83

Merged error: 3.2b

Counts

83 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
1.0b	(+ (* t t) (/ l (/ x l)))
4.4b	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
24.9b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-sqr-sqrt` `associate-l` `add-cbrt-cube`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r/` `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))))
10.0ms	(+ (* t t) (/ l (/ x l)))
10.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
9.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
9.0ms	(+ (* t t) (/ l (/ x l)))
14.0ms	(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify26.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5001	1386

prune202.0ms

Filtered

60 candidates to 79 candidates (-31.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	77	13	90

Merged error: 3.2b

Counts

90 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

24.9b	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (* (cbrt (+ (* t t) (* l (/ l x)))) (cbrt (+ (* t t) (* l (/ l x))))) (cbrt (+ (* t t) (* l (/ l x))))))))
25.6b	(cbrt (+ (* t t) (* l (/ l x))))
25.6b	(cbrt (+ (* t t) (* l (/ l x))))
25.6b	(cbrt (+ (* t t) (* l (/ l x))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div` `associate-*r/`
31×	`flip3-+` `flip-+`
28×	`frac-times` `sqrt-div`
26×	`frac-add`
14×	`associate-*l/`
9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 80

Calls

4 calls:

16.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (* (cbrt (+ (* t t) (* l (/ l x)))) (cbrt (+ (* t t) (* l (/ l x))))) (cbrt (+ (* t t) (* l (/ l x))))))))
4.0ms	(cbrt (+ (* t t) (* l (/ l x))))
4.0ms	(cbrt (+ (* t t) (* l (/ l x))))
4.0ms	(cbrt (+ (* t t) (* l (/ l x))))

series111.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (* (* (cbrt (+ (* t t) (* l (/ l x)))) (cbrt (+ (* t t) (* l (/ l x))))) (cbrt (+ (* t t) (* l (/ l x))))))))
26.0ms	(cbrt (+ (* t t) (* l (/ l x))))
26.0ms	(cbrt (+ (* t t) (* l (/ l x))))
31.0ms	(cbrt (+ (* t t) (* l (/ l x))))

simplify54.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5292	4034

prune359.0ms

Filtered

70 candidates to 92 candidates (-31.4%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	91	14	105

Merged error: 3.2b

Counts

105 → 14

regimes691.0ms

Accuracy

77.9% (5.1b remaining)

Error of 9.0b against oracle of 3.9b and baseline of 27.0b

bsearch523.0ms

Steps

Iters	Range		Point
8	1.8136085978804598e+139	3.674489611550249e+143	1.0554869999757181e+141
9	2.7168785140288987e-163	1.7591283665603802e-157	2.7429969138306416e-163
9	1.3403035055972665e-188	1.0470280067365474e-182	1.032669005686797e-182
3	-6.465359169875676e-231	-4.6573883160409133e-231	-6.321390322783704e-231
9	-4.3999150322774637e-178	-1.352521393981598e-183	-1.3693872748817779e-183
9	-4.8551511605139105e+88	-8.917950600087324e+80	-4.775439244147404e+88

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	160	188
1	160	188

end0.0ms

sample1.9s

Algorithm

intervals

Results

375.0ms	5098×	body	80	valid
284.0ms	854×	body	1280	valid
273.0ms	1039×	body	640	valid
198.0ms	606×	body	1280	nan
151.0ms	585×	body	640	nan
124.0ms	624×	body	320	valid
97.0ms	1369×	body	80	nan
63.0ms	327×	body	320	nan
54.0ms	385×	body	160	valid
32.0ms	188×	body	160	nan

Details

analyze782.0ms

sample63.0ms

simplify35.0ms

prune11.0ms

localize16.0ms

rewrite53.0ms

series343.0ms

simplify45.0ms

prune216.0ms

localize16.0ms

rewrite38.0ms

series52.0ms

simplify29.0ms

prune171.0ms

localize18.0ms

rewrite40.0ms

series53.0ms

simplify26.0ms

prune202.0ms

localize24.0ms

rewrite33.0ms

series111.0ms

simplify54.0ms

prune359.0ms

regimes691.0ms

bsearch523.0ms

simplify3.0ms

end0.0ms

sample1.9s

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