Details

sample486.0ms

Algorithm

intervals

Results

83.0ms	275×	body	80	nan
15.0ms	165×	body	80	valid
11.0ms	24×	body	1280	valid
11.0ms	29×	body	640	valid
7.0ms	21×	body	640	nan
7.0ms	14×	body	1280	nan
6.0ms	23×	body	320	valid
3.0ms	15×	body	160	valid
2.0ms	10×	body	320	nan
1.0ms	6×	body	160	nan

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3799
6	1449
5	797
4	423
3	199
2	93
1	39
0	18

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 45.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 2.0) (/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t))
0.3b	(/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t)
13.7b	(- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
23.9b	(sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity` `add-cube-cbrt`
147×	`sqrt-prod`
25×	`associate-/r*`
12×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `sqrt-div` `div-exp`
3×	`flip3--` `flip--`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 243

Calls

4 calls:

63.0ms	(/ (sqrt 2.0) (/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t))
89.0ms	(/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t)
46.0ms	(- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
65.0ms	(sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

series2.1s

Counts

4 → 12

Calls

4 calls:

690.0ms	(/ (sqrt 2.0) (/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t))
549.0ms	(/ (sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))) t)
336.0ms	(- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l))
517.0ms	(sqrt (- (* (+ (* (* t t) 2.0) (* l l)) (/ (+ 1.0 x) (- x 1.0))) (* l l)))

simplify2.2s

Counts

255 → 255

Iterations

Iter	Nodes
done	5000
2	4821
1	873
0	336

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

localize42.0ms

Local error

Found 4 expressions with local error:

5.9b	(+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0)))
6.2b	(/ (* 2.0 (* l l)) x)
9.9b	(/ x (* t t))
29.7b	(sqrt (+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0))))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
13×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `add-log-exp`
6×	`times-frac`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`associate-/r` `flip3-+` `sqrt-div` `frac-add` `prod-exp` `sqrt-prod` `cbrt-unprod` `flip-+` `associate-/l`
3×	`sum-log`
2×	`clear-num` `frac-2neg` `div-inv` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `associate-+r+` `sqrt-pow1` `pow1/2`

Counts

4 → 78

Calls

4 calls:

103.0ms	(+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0)))
17.0ms	(/ (* 2.0 (* l l)) x)
6.0ms	(/ x (* t t))
161.0ms	(sqrt (+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0)))
43.0ms	(/ (* 2.0 (* l l)) x)
30.0ms	(/ x (* t t))
406.0ms	(sqrt (+ (/ 4.0 (/ x (* t t))) (+ (/ (* 2.0 (* l l)) x) (* (* t t) 2.0))))

simplify1.8s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	3883
1	559
0	179

prune680.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize99.0ms

Local error

Found 4 expressions with local error:

6.3b	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
6.3b	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
29.7b	(sqrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))
29.7b	(sqrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))

rewrite5.0s

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `sum-log` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+`
2×	`+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2`

Counts

4 → 56

Calls

4 calls:

1.2s	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
1.2s	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
1.3s	(sqrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))
1.3s	(sqrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

97.0ms	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
93.0ms	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
557.0ms	(sqrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))
516.0ms	(sqrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))

simplify735.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
2	1015
1	221
0	86

prune816.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.2b

localize66.0ms

Local error

Found 4 expressions with local error:

6.3b	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
6.3b	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
30.7b	(cbrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))
30.7b	(cbrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))

rewrite3.7s

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
6×	`cbrt-prod` `add-sqr-sqrt` `sum-log` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `cbrt-div` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
2×	`+-commutative` `associate-+l+` `pow1/3`

Counts

4 → 52

Calls

4 calls:

1.2s	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
1.2s	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
626.0ms	(cbrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))
666.0ms	(cbrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))

series833.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
97.0ms	(+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0)))
313.0ms	(cbrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))
302.0ms	(cbrt (+ (+ (/ (* l 2.0) (/ x l)) (/ 4.0 (/ (/ x t) t))) (* t (* t 2.0))))

simplify553.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	1007
1	266
0	113

prune865.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 3.2b

regimes903.0ms

Accuracy

76.1% (5.7b remaining)

Error of 9.8b against oracle of 4.1b and baseline of 27.9b

bsearch1.0s

Steps

Iters	Range		Point
9	2.3682169563964882e+42	1.376222274811364e+49	5.469601309486937e+45
8	1.7412922778296343e-165	2.5725953662274735e-162	6.783164823431965e-165
11	9.485480553618113e-206	2.7798908565106377e-186	3.4247796977069794e-203
10	-2.3531295468621075e+92	-8.259027920981738e+77	-2.2425439320166414e+86

simplify14.0ms

Iterations

Iter	Nodes
done	87
3	87
2	82
1	73
0	54

end0.0ms

sample6.6s

Algorithm

intervals

Results

1.9s	10170×	body	80	nan
995.0ms	1029×	body	640	valid
947.0ms	875×	body	1280	valid
592.0ms	5053×	body	80	valid
315.0ms	663×	body	320	valid
283.0ms	579×	body	640	nan
277.0ms	571×	body	1280	nan
137.0ms	336×	body	320	nan
77.0ms	380×	body	160	valid
40.0ms	223×	body	160	nan