Details

sample422.0ms

Algorithm

intervals

Results

156.0ms	175×	body	80	valid
44.0ms	277×	body	80	nan
19.0ms	34×	body	640	valid
14.0ms	19×	body	1280	nan
13.0ms	22×	body	640	nan
12.0ms	16×	body	1280	valid
8.0ms	21×	body	320	valid
4.0ms	10×	body	320	nan
3.0ms	8×	body	160	nan
2.0ms	10×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5007
7	2272
6	1130
5	629
4	364
3	179
2	90
1	39
0	18

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

localize78.0ms

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)
12.5b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.8b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite316.0ms

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:

119.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
21.0ms	(* (sqrt 2.0) t)
62.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
102.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series4.0s

Counts

4 → 12

Calls

4 calls:

809.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
81.0ms	(* (sqrt 2.0) t)
414.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
2.7s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1610
1	447
0	168

prune949.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.1b

localize77.0ms

Local error

Found 4 expressions with local error:

3.6b	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
6.2b	(/ (* l l) x)
10.3b	(/ x (* t t))
25.5b	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

57.0ms	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
20.0ms	(/ (* l l) x)
16.0ms	(/ x (* t t))
100.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t))))
36.0ms	(/ (* l l) x)
48.0ms	(/ x (* t t))
464.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (* l l) x))) (/ 4.0 (/ x (* t t)))))

simplify2.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1984
1	499
0	170

prune857.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.5b

localize125.0ms

Local error

Found 4 expressions with local error:

1.3b	(/ (* (/ l (cbrt x)) (/ l (cbrt x))) (cbrt x))
3.6b	(+ (* 2.0 (+ (* t t) (/ (* (/ l (cbrt x)) (/ l (cbrt x))) (cbrt x)))) (/ 4.0 (/ x (* t t))))
10.3b	(/ x (* t t))
25.5b	(sqrt (+ (* 2.0 (+ (* t t) (/ (* (/ l (cbrt x)) (/ l (cbrt x))) (cbrt x)))) (/ 4.0 (/ x (* t t)))))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

43.0ms	(/ (* (/ l (cbrt x)) (/ l (cbrt x))) (cbrt x))
60.0ms	(+ (* 2.0 (+ (* t t) (/ (* (/ l (cbrt x)) (/ l (cbrt x))) (cbrt x)))) (/ 4.0 (/ x (* t t))))
17.0ms	(/ x (* t t))
103.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (* (/ l (cbrt x)) (/ l (cbrt x))) (cbrt x)))) (/ 4.0 (/ x (* t t)))))

series810.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (* (/ l (cbrt x)) (/ l (cbrt x))) (cbrt x))
169.0ms	(+ (* 2.0 (+ (* t t) (/ (* (/ l (cbrt x)) (/ l (cbrt x))) (cbrt x)))) (/ 4.0 (/ x (* t t))))
46.0ms	(/ x (* t t))
516.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (* (/ l (cbrt x)) (/ l (cbrt x))) (cbrt x)))) (/ 4.0 (/ x (* t t)))))

simplify2.9s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	2030
1	586
0	203

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.5b

localize209.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (* t t) (* (/ (/ l (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))) (/ (/ l (cbrt x)) (cbrt (cbrt x)))))
3.6b	(+ (* 2.0 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))) (/ (/ l (cbrt x)) (cbrt (cbrt x)))))) (/ 4.0 (/ x (* t t))))
10.3b	(/ x (* t t))
25.5b	(sqrt (+ (* 2.0 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))) (/ (/ l (cbrt x)) (cbrt (cbrt x)))))) (/ 4.0 (/ x (* t t)))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

19.0ms	(+ (* t t) (* (/ (/ l (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))) (/ (/ l (cbrt x)) (cbrt (cbrt x)))))
53.0ms	(+ (* 2.0 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))) (/ (/ l (cbrt x)) (cbrt (cbrt x)))))) (/ 4.0 (/ x (* t t))))
16.0ms	(/ x (* t t))
83.0ms	(sqrt (+ (* 2.0 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))) (/ (/ l (cbrt x)) (cbrt (cbrt x)))))) (/ 4.0 (/ x (* t t)))))

series929.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (* t t) (* (/ (/ l (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))) (/ (/ l (cbrt x)) (cbrt (cbrt x)))))
189.0ms	(+ (* 2.0 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))) (/ (/ l (cbrt x)) (cbrt (cbrt x)))))) (/ 4.0 (/ x (* t t))))
40.0ms	(/ x (* t t))
564.0ms	(sqrt (+ (* 2.0 (+ (* t t) (* (/ (/ l (cbrt x)) (cbrt (* (cbrt x) (cbrt x)))) (/ (/ l (cbrt x)) (cbrt (cbrt x)))))) (/ 4.0 (/ x (* t t)))))

simplify3.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
2	1694
1	439
0	156

prune994.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.5b

regimes1.2s

Accuracy

77% (5.3b remaining)

Error of 9.3b against oracle of 3.9b and baseline of 27.2b

bsearch313.0ms

Steps

Iters	Range		Point
5	1.4232709391104353e+72	3.448040286260833e+72	2.8189485200434593e+72
5	-6.434131299274751e+123	-3.143476380631542e+123	-4.290053800826923e+123

simplify35.0ms

Iterations

Iter	Nodes
done	65
1	65
0	50

end0.0ms

sample8.0s

Algorithm

intervals

Results

2.2s	10108×	body	80	nan
1.2s	5094×	body	80	valid
906.0ms	648×	body	640	nan
891.0ms	877×	body	1280	valid
745.0ms	951×	body	640	valid
383.0ms	583×	body	1280	nan
378.0ms	690×	body	320	valid
172.0ms	388×	body	160	valid
122.0ms	334×	body	320	nan
106.0ms	195×	body	160	nan