Details

sample83.0ms

Algorithm

intervals

Results

24.0ms	315×	body	80	nan
9.0ms	168×	body	80	valid
7.0ms	36×	body	640	valid
6.0ms	23×	body	1280	valid
5.0ms	20×	body	1280	nan
4.0ms	22×	body	640	nan
2.0ms	14×	body	320	valid
1.0ms	15×	body	160	valid
1.0ms	9×	body	320	nan
1.0ms	6×	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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize19.0ms

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)
15.0b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite71.0ms

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:

30.0ms	(/ (* (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)
12.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

416.0ms	(/ (* (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)
210.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.1s	(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	1207
1	2051	1099
2	5002	1094

prune289.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 6.1b

localize17.0ms

Local error

Found 4 expressions with local error:

5.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.9b	(/ (pow t 2) x)
6.9b	(/ (pow l 2) x)
27.7b	(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:

8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.0ms	(/ (pow t 2) x)
4.0ms	(/ (pow l 2) x)
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify61.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (48.0ms)

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

prune446.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (pow t 2) (* l (/ l x)))
5.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
6.9b	(/ (pow t 2) x)
27.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
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`

Counts

4 → 92

Calls

4 calls:

6.0ms	(+ (pow t 2) (* l (/ l x)))
8.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
4.0ms	(/ (pow t 2) x)
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (pow t 2) (* l (/ l x)))
66.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
18.0ms	(/ (pow t 2) x)
159.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify58.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	456	925
1	1936	858
2	5001	855

prune325.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
5.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
6.9b	(/ (pow t 2) x)
27.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
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`

Counts

4 → 92

Calls

4 calls:

6.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
11.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
4.0ms	(/ (pow t 2) x)
9.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
82.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
18.0ms	(/ (pow t 2) x)
177.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	463	1308
1	1965	1213
2	5001	1210

prune345.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.2b

regimes381.0ms

Accuracy

75.5% (6.0b remaining)

Error of 9.8b against oracle of 3.9b and baseline of 28.2b

bsearch490.0ms

Steps

Iters	Range		Point
9	8249416806277068.0	6.908956904862703e+24	6.769189022626266e+24
9	-5.149414502062706e-287	-6.479421214823862e-296	-5.07338813022938e-287
9	-1.9154334448410318e-177	-2.122947083583308e-184	-3.37568701424073e-181
8	-7.474441928331378e+61	-1.7381937350890755e+58	-8.171560713962325e+60

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	97
1	67	97
2	67	97

end0.0ms

sample2.1s

Algorithm

intervals

Results

497.0ms	10142×	body	80	nan
271.0ms	5082×	body	80	valid
234.0ms	879×	body	1280	valid
199.0ms	994×	body	640	valid
143.0ms	587×	body	1280	nan
114.0ms	590×	body	640	nan
95.0ms	649×	body	320	valid
45.0ms	316×	body	320	nan
39.0ms	396×	body	160	valid
21.0ms	217×	body	160	nan