Details

sample485.0ms

Algorithm

intervals

Results

61.0ms	347×	body	80	nan
53.0ms	21×	body	1280	valid
29.0ms	171×	body	80	valid
24.0ms	33×	body	640	valid
18.0ms	24×	body	1280	nan
13.0ms	18×	body	640	nan
10.0ms	22×	body	320	valid
8.0ms	18×	body	320	nan
5.0ms	9×	body	160	valid
2.0ms	7×	body	160	nan

simplify966.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
6	2002
5	1119
4	393
3	181
2	93
1	42
0	18

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize82.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.5b	(* (sqrt 2) t)
13.0b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.8b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`sqrt-div` `insert-posit16`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

85.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
15.0ms	(* (sqrt 2) t)
48.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
48.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.4s

Counts

4 → 12

Calls

4 calls:

447.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
74.0ms	(* (sqrt 2) t)
275.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.6s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	2022
3	2022
2	1525
1	458
0	170

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.0b

localize37.0ms

Local error

Found 4 expressions with local error:

4.2b	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
4.5b	(/ (* l l) x)
8.4b	(/ (* t t) x)
29.4b	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `div-exp` `associate-l/` `frac-add` `associate-r/` `flip-+` `insert-posit16`
3×	`sqrt-prod`
2×	`associate-+l+` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 78

Calls

4 calls:

39.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
22.0ms	(/ (* l l) x)
18.0ms	(/ (* t t) x)
31.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series782.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
21.0ms	(/ (* l l) x)
21.0ms	(/ (* t t) x)
652.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify937.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	2000
2	2000
1	536
0	172

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2) t)
4.2b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
8.4b	(/ (* t t) x)
29.4b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l` `add-log-exp`
4×	`flip3-+` `sqrt-div` `associate-l/` `frac-add` `associate-r/` `flip-+` `insert-posit16`
3×	`associate-/r` `times-frac` `associate-r*`
2×	`cbrt-undiv` `associate-+l+` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 79

Calls

4 calls:

9.0ms	(* (sqrt 2) t)
30.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
18.0ms	(/ (* t t) x)
48.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sqrt 2) t)
98.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
26.0ms	(/ (* t t) x)
351.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify983.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	2000
2	2000
1	498
0	171

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* t t) (/ l (/ x l)))
4.2b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
8.4b	(/ (* t t) x)
29.4b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `associate-l/` `frac-add` `associate-r/` `insert-posit16`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `+-commutative` `associate-+l+` `sum-log` `div-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

10.0ms	(+ (* t t) (/ l (/ x l)))
24.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
12.0ms	(/ (* t t) x)
34.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (* t t) (/ l (/ x l)))
86.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
34.0ms	(/ (* t t) x)
285.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify1.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	2002
3	2002
2	1831
1	462
0	155

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

regimes656.0ms

Accuracy

77.4% (5.3b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 27.5b

bsearch933.0ms

Steps

Iters	Range		Point
5	6.262036766516395e+134	1.782199942337008e+135	1.0888219445242733e+135
8	3.907881210716465e-189	1.576407217143116e-185	9.831366213789788e-187
8	4.056079679036218e-287	4.597436613380927e-284	3.4759257316157413e-284
4	-5.516853907540803e+62	-3.19405123701085e+62	-5.415525381702613e+62

simplify31.0ms

Iterations

Iter	Nodes
done	74
1	74
0	55

end0.0ms

sample9.0s

Algorithm

intervals

Results

2.3s	10386×	body	80	nan
1.6s	5227×	body	80	valid
1.1s	608×	body	1280	nan
903.0ms	982×	body	640	valid
867.0ms	804×	body	1280	valid
721.0ms	641×	body	320	valid
477.0ms	587×	body	640	nan
253.0ms	352×	body	320	nan
149.0ms	346×	body	160	valid
62.0ms	168×	body	160	nan