Details

sample74.0ms

Algorithm

intervals

Results

16.0ms	317×	body	80	nan
9.0ms	173×	body	80	valid
6.0ms	25×	body	1280	valid
6.0ms	30×	body	640	valid
5.0ms	21×	body	1280	nan
4.0ms	22×	body	640	nan
3.0ms	22×	body	320	valid
1.0ms	10×	body	320	nan
1.0ms	7×	body	160	nan
1.0ms	6×	body	160	valid

simplify94.0ms

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: 38.9b

Counts

2 → 1

localize18.0ms

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)
9.5b	(- (* (/ (+ 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)))

rewrite285.0ms

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:

88.0ms	(/ (* (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)
69.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
75.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

444.0ms	(/ (* (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)
228.0ms	(- (* (/ (+ 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)))

simplify213.0ms

Algorithm

egg-herbie

Counts

560 → 560

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	1111	13941
1	4267	13734
2	5001	13550

prune809.0ms

Filtered

560 candidates to 204 candidates (36.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	555	5	560
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	556	5	561

Merged error: 4.6b

Counts

561 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
4.6b	(/ (pow l 2) x)
7.3b	(/ (pow t 2) x)
23.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite125.0ms

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:

51.0ms	(+ (* 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)))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
178.0ms	(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	1026	3303
1	4354	3183
2	5001	3183

prune535.0ms

Filtered

212 candidates to 131 candidates (61.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	208	4	212
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	209	8	217

Merged error: 2.8b

Counts

217 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
7.3b	(/ (pow t 2) x)
23.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite125.0ms

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:

7.0ms	(* (sqrt 2.0) t)
50.0ms	(+ (* 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))))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (sqrt 2.0) t)
71.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
19.0ms	(/ (pow t 2) x)
173.0ms	(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	982	3150
1	4473	3050
2	5001	3050

prune472.0ms

Filtered

185 candidates to 113 candidates (61.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	182	3	185
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	185	8	193

Merged error: 2.8b

Counts

193 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow t 2) (* l (/ l x)))
4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
7.3b	(/ (pow t 2) x)
23.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite138.0ms

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:

15.0ms	(+ (pow t 2) (* l (/ l x)))
55.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
5.0ms	(/ (pow t 2) x)
53.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series303.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (pow t 2) (* l (/ l x)))
71.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
19.0ms	(/ (pow t 2) x)
173.0ms	(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 (23.0ms)

Iter	Nodes	Cost
0	959	3169
1	4154	3065
2	5001	3065

prune490.0ms

Filtered

176 candidates to 110 candidates (62.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	174	10	184

Merged error: 2.8b

Counts

184 → 10

regimes250.0ms

Accuracy

76% (5.7b remaining)

Error of 9.3b against oracle of 3.6b and baseline of 27.3b

bsearch153.0ms

Steps

Iters	Range		Point
5	5.154913321084455e+64	1.0494475940676383e+65	9.728032582279225e+64
7	-5.11343594011913e+52	-2.8338919889536108e+51	-1.1759228276149934e+52

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	64
1	66	64

end0.0ms

sample2.1s

Algorithm

intervals

Results

503.0ms	9991×	body	80	nan
278.0ms	5190×	body	80	valid
212.0ms	822×	body	1280	valid
203.0ms	1022×	body	640	valid
147.0ms	603×	body	1280	nan
113.0ms	569×	body	640	nan
91.0ms	625×	body	320	valid
51.0ms	361×	body	320	nan
33.0ms	341×	body	160	valid
18.0ms	190×	body	160	nan