Details

sample98.0ms

Algorithm

intervals

Results

28.0ms	313×	body	80	nan
13.0ms	180×	body	80	valid
8.0ms	24×	body	1280	valid
8.0ms	27×	body	640	valid
6.0ms	17×	body	1280	nan
4.0ms	16×	body	640	nan
3.0ms	13×	body	320	valid
2.0ms	9×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	6×	body	160	nan

simplify88.0ms

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: 41.9b

Counts

2 → 1

localize26.0ms

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)
12.2b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
22.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite55.0ms

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 → 80

Calls

4 calls:

17.0ms	(/ (* (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)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
16.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

425.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
39.0ms	(* (sqrt 2.0) t)
217.0ms	(- (* (/ (+ 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)))

simplify62.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	417	1208
1	2051	1099
2	5002	1094

prune288.0ms

Filtered

92 candidates to 65 candidates (70.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 5.0b

Counts

93 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

3.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.3b	(/ (pow l 2) x)
9.2b	(/ (pow t 2) x)
26.6b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

9.0ms	(+ (* 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)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
17.0ms	(/ (pow l 2) x)
23.0ms	(/ (pow t 2) x)
159.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	526	1093
1	2235	984
2	5001	978

prune410.0ms

Filtered

142 candidates to 97 candidates (68.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	138	10	148

Merged error: 1.9b

Counts

148 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (pow t 2) (/ l (/ x l)))
3.4b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
9.2b	(/ (pow t 2) x)
26.6b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

20.0ms	(+ (pow t 2) (/ l (/ x l)))
13.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
5.0ms	(/ (pow t 2) x)
7.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (pow t 2) (/ l (/ x l)))
65.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
18.0ms	(/ (pow t 2) x)
160.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	453	932
1	1835	862
2	5002	859

prune311.0ms

Filtered

105 candidates to 76 candidates (72.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	105	10	115

Merged error: 1.9b

Counts

115 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

9.2b	(/ (pow t 2) x)
9.2b	(/ (pow t 2) x)
27.4b	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))
27.4b	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`cbrt-div` `associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`cbrt-prod` `div-exp` `associate-/r*`
4×	`pow1` `flip3-+` `frac-add` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow1/3` `pow-exp` `clear-num` `div-inv`

Counts

4 → 128

Calls

4 calls:

8.0ms	(/ (pow t 2) x)
5.0ms	(/ (pow t 2) x)
7.0ms	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))
8.0ms	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow t 2) x)
24.0ms	(/ (pow t 2) x)
209.0ms	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))
212.0ms	(cbrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	420	1242
1	1566	1142
2	5001	1130

prune523.0ms

Filtered

140 candidates to 98 candidates (70.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	139	11	150

Merged error: 1.9b

Counts

150 → 11

regimes540.0ms

Accuracy

76.7% (5.7b remaining)

Error of 9.5b against oracle of 3.8b and baseline of 28.2b

bsearch366.0ms

Steps

Iters	Range		Point
7	1.56125050185529e+80	3.1097064741089316e+81	6.92955347104013e+80
7	-1.9014569726683186e-283	-3.019842982184082e-285	-1.7759758079123057e-283
3	-9.137979276603949e-166	-7.229263141007501e-166	-9.018684518129172e-166
7	-1.0775817463235446e+74	-4.492037802898764e+71	-9.556193700399798e+73

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	92
1	65	92

end0.0ms

sample2.7s

Algorithm

intervals

Results

707.0ms	10042×	body	80	nan
361.0ms	5137×	body	80	valid
294.0ms	824×	body	1280	valid
274.0ms	1007×	body	640	valid
199.0ms	561×	body	1280	nan
174.0ms	640×	body	640	nan
139.0ms	684×	body	320	valid
73.0ms	357×	body	320	nan
47.0ms	348×	body	160	valid
23.0ms	170×	body	160	nan