Details

sample76.0ms

Algorithm

intervals

Results

16.0ms	317×	body	80	nan
9.0ms	165×	body	80	valid
8.0ms	32×	body	1280	valid
6.0ms	29×	body	640	valid
5.0ms	24×	body	640	nan
3.0ms	13×	body	1280	nan
3.0ms	18×	body	320	valid
1.0ms	10×	body	320	nan
1.0ms	12×	body	160	valid
1.0ms	7×	body	160	nan

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	14
1	93	14
2	193	14
3	414	14
4	718	14
5	1192	14
6	2816	14
7	5001	14

prune5.0ms

Filtered

1 candidates to 0 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: 40.1b

Counts

2 → 1

localize29.0ms

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)
11.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
18.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

1110×	`add-sqr-sqrt`
504×	`sqrt-prod`
495×	`times-frac`
301×	`unswap-sqr`
298×	`*-un-lft-identity`
285×	`difference-of-squares`
238×	`associate-l`
146×	`add-cube-cbrt`
84×	`*-commutative`
81×	`associate-r`
76×	`distribute-lft-out--`
57×	`swap-sqr`
25×	`associate-/r*`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
4×	`sqrt-div` `associate--l+`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `div-inv`

Counts

4 → 548

Calls

4 calls:

86.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
69.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
73.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

435.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
41.0ms	(* (sqrt 2.0) t)
215.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify212.0ms

Algorithm

egg-herbie

Counts

560 → 560

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	1119	13941
1	4335	13734
2	5001	13550

prune993.0ms

Filtered

560 candidates to 204 candidates (36.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	554	6	560
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	555	6	561

Merged error: 7.1b

Counts

561 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

2.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
4.3b	(/ (pow l 2) x)
6.7b	(/ (pow t 2) x)
24.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

120×	`associate-*r/`
71×	`*-un-lft-identity`
64×	`frac-add`
52×	`add-sqr-sqrt` `associate-/l*`
51×	`add-cube-cbrt`
48×	`times-frac`
36×	`unpow-prod-down`
34×	`flip3-+` `sqrt-div` `flip-+`
18×	`associate-/r*`
14×	`add-exp-log`
12×	`unpow2` `sqr-pow`
10×	`clear-num`
8×	`associate-l` `un-div-inv` `add-cbrt-cube` `distribute-lft-out`
7×	`sqrt-prod`
6×	`frac-2neg` `div-exp` `add-log-exp`
5×	`pow1`
4×	`associate-+r+`
3×	`+-commutative`
2×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 200

Calls

4 calls:

53.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms	(/ (pow l 2) x)
5.0ms	(/ (pow t 2) x)
52.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series269.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
165.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify129.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1038	3353
1	4741	3183
2	5002	3183

prune662.0ms

Filtered

212 candidates to 131 candidates (61.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	204	8	212
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	206	12	218

Merged error: 4.7b

Counts

218 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
2.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
6.7b	(/ (pow t 2) x)
24.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

120×	`associate-*r/`
64×	`frac-add`
57×	`*-un-lft-identity`
44×	`associate-/l*`
42×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
34×	`flip3-+` `sqrt-div` `flip-+`
24×	`unpow-prod-down` `times-frac`
15×	`associate-/r*`
14×	`associate-l`
11×	`add-exp-log` `sqrt-prod`
9×	`clear-num`
8×	`un-div-inv` `add-cbrt-cube` `distribute-lft-out` `unpow2` `sqr-pow`
7×	`pow1`
6×	`add-log-exp`
5×	`frac-2neg`
4×	`associate-+r+`
3×	`+-commutative` `div-exp` `associate-r`
2×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 173

Calls

4 calls:

4.0ms	(* (sqrt 2.0) t)
54.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
5.0ms	(/ (pow t 2) x)
54.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sqrt 2.0) t)
64.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
25.0ms	(/ (pow t 2) x)
171.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify142.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	994	3150
1	4556	3050
2	5001	3050

prune561.0ms

Filtered

185 candidates to 112 candidates (60.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	182	3	185
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	186	11	197

Merged error: 4.7b

Counts

197 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow t 2) (* l (/ l x)))
2.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
6.7b	(/ (pow t 2) x)
24.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

120×	`associate-*r/`
64×	`frac-add`
58×	`*-un-lft-identity`
44×	`associate-/l*`
35×	`add-sqr-sqrt` `flip3-+` `flip-+`
34×	`add-cube-cbrt` `sqrt-div`
24×	`unpow-prod-down` `times-frac`
15×	`associate-/r*`
10×	`distribute-lft-out`
9×	`add-exp-log` `associate-l` `clear-num`
8×	`un-div-inv` `unpow2` `add-log-exp` `sqr-pow`
7×	`sqrt-prod`
6×	`add-cbrt-cube`
5×	`pow1` `frac-2neg`
4×	`+-commutative` `associate-+r+`
3×	`div-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `sum-log`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `div-inv`

Counts

4 → 164

Calls

4 calls:

18.0ms	(+ (pow t 2) (* l (/ l x)))
53.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
7.0ms	(/ (pow t 2) x)
56.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (pow t 2) (* l (/ l x)))
62.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
18.0ms	(/ (pow t 2) x)
169.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify128.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	972	3169
1	4242	3065
2	5001	3065

prune557.0ms

Filtered

176 candidates to 110 candidates (62.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	172	4	176
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	175	12	187

Merged error: 4.7b

Counts

187 → 12

regimes438.0ms

Accuracy

77.6% (5.4b remaining)

Error of 9.3b against oracle of 4.0b and baseline of 27.9b

bsearch334.0ms

Steps

Iters	Range		Point
8	1.2904779615766892e+141	7.028027817791006e+144	5.060853302910058e+141
5	-1.4953326436467958e-263	-4.242125608336209e-264	-1.4728195123242452e-263
5	-6.754176268358103e-154	-3.315251958224177e-154	-3.3628327780434735e-154
8	-3.707972559077159e+126	-1.5456767356727216e+123	-3.628554763998337e+123

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	87
1	64	87
2	64	87

end0.0ms

sample2.1s

Algorithm

intervals

Results

524.0ms	10105×	body	80	nan
262.0ms	5029×	body	80	valid
233.0ms	883×	body	1280	valid
218.0ms	1064×	body	640	valid
144.0ms	556×	body	1280	nan
118.0ms	590×	body	640	nan
102.0ms	668×	body	320	valid
52.0ms	341×	body	320	nan
36.0ms	356×	body	160	valid
18.0ms	186×	body	160	nan