Details

sample89.0ms

Algorithm

intervals

Results

26.0ms	340×	body	80	nan
8.0ms	161×	body	80	valid
8.0ms	29×	body	1280	valid
6.0ms	32×	body	640	valid
5.0ms	27×	body	640	nan
5.0ms	21×	body	1280	nan
4.0ms	23×	body	320	valid
2.0ms	14×	body	320	nan
1.0ms	11×	body	160	valid
0.0ms	4×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

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))))
0.5b	(* (sqrt 2.0) t)
13.7b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.9b	(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 → 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))
15.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

410.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
43.0ms	(* (sqrt 2.0) t)
207.0ms	(- (* (/ (+ 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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	417	1207
1	2051	1099
2	5002	1094

prune310.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.2b	(/ (pow l 2) x)
9.9b	(/ (pow t 2) x)
27.6b	(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)))))

series260.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms	(/ (pow l 2) x)
21.0ms	(/ (pow t 2) x)
159.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (48.0ms)

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

prune480.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (pow t 2) (/ l (/ x l)))
3.8b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
9.9b	(/ (pow t 2) x)
27.6b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite44.0ms

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)))
9.0ms	(+ (* 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))))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (pow t 2) (/ l (/ x l)))
64.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
18.0ms	(/ (pow t 2) x)
158.0ms	(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 (45.0ms)

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

prune376.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.8b

localize20.0ms

Local error

Found 4 expressions with local error:

9.9b	(/ (pow t 2) x)
9.9b	(/ (pow t 2) x)
27.6b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))
27.6b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

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

series350.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow t 2) x)
18.0ms	(/ (pow t 2) x)
156.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))
158.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	381	1124
1	1536	1046
2	5003	1040

prune592.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

regimes506.0ms

Accuracy

75.5% (5.9b remaining)

Error of 9.8b against oracle of 3.9b and baseline of 28.0b

bsearch153.0ms

Steps

Iters	Range		Point
8	0.20768356118646913	6803.479780933057	6683.483482401855
5	-8.662603811930578e+142	-2.4793126303145234e+142	-2.8145357030164877e+142

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	64
1	63	64

end0.0ms

sample2.0s

Algorithm

intervals

Results

489.0ms	9863×	body	80	nan
261.0ms	5077×	body	80	valid
210.0ms	853×	body	1280	valid
197.0ms	1014×	body	640	valid
146.0ms	596×	body	1280	nan
111.0ms	570×	body	640	nan
102.0ms	701×	body	320	valid
57.0ms	393×	body	320	nan
36.0ms	355×	body	160	valid
18.0ms	189×	body	160	nan