Details

sample90.0ms

Algorithm

intervals

Results

18.0ms	337×	body	80	nan
15.0ms	160×	body	80	valid
8.0ms	35×	body	640	valid
7.0ms	27×	body	1280	valid
5.0ms	24×	body	640	nan
5.0ms	17×	body	1280	nan
4.0ms	23×	body	320	valid
3.0ms	17×	body	320	nan
1.0ms	11×	body	160	valid
1.0ms	10×	body	160	nan

simplify87.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.2b

localize20.0ms

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)
14.3b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.5b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite76.0ms

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:

25.0ms	(/ (* (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)
18.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
24.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

430.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
40.0ms	(* (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 (50.0ms)

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

prune324.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.4b

localize18.0ms

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))))
6.7b	(/ (pow l 2) x)
10.5b	(/ (pow t 2) x)
28.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite33.0ms

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))))
4.0ms	(/ (pow l 2) x)
5.0ms	(/ (pow t 2) x)
10.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
22.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
167.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (50.0ms)

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

prune480.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize17.0ms

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)))))
10.5b	(/ (pow t 2) x)
28.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
4.0ms	(/ (pow t 2) x)
12.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (sqrt 2.0) t)
65.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
19.0ms	(/ (pow t 2) x)
160.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	478	927
1	2222	851
2	5002	848

prune382.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
4.0b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
10.5b	(/ (pow t 2) x)
28.1b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

22.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
9.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
4.0ms	(/ (pow t 2) x)
10.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
65.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
18.0ms	(/ (pow t 2) x)
162.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify71.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	529	1090
1	2367	937
2	5001	895

prune371.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.4b

regimes471.0ms

Accuracy

77.8% (5.3b remaining)

Error of 9.3b against oracle of 4.0b and baseline of 27.7b

bsearch492.0ms

Steps

Iters	Range		Point
10	4.004698128300931e+101	6.850788834278051e+120	7.905755421666351e+116
9	1.4466336082644377e-172	2.9642073903192953e-167	2.9350109141003192e-167
10	1.9462428459118174e-233	6.595345726533069e-219	3.43051773656449e-229
7	-3.3952783159900906e+79	-1.663444366923187e+78	-3.244180928128228e+79

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	106
1	78	106
2	81	106
3	81	106

end0.0ms

sample2.2s

Algorithm

intervals

Results

534.0ms	10008×	body	80	nan
285.0ms	5103×	body	80	valid
241.0ms	884×	body	1280	valid
216.0ms	990×	body	640	valid
154.0ms	598×	body	1280	nan
121.0ms	586×	body	640	nan
105.0ms	677×	body	320	valid
53.0ms	350×	body	320	nan
38.0ms	346×	body	160	valid
21.0ms	209×	body	160	nan