Details

sample795.0ms

Algorithm

intervals

Results

202.0ms	39×	body	1280	valid
162.0ms	343×	body	80	nan
84.0ms	154×	body	80	valid
59.0ms	26×	body	640	valid
28.0ms	22×	body	640	nan
26.0ms	20×	body	1280	nan
22.0ms	24×	body	320	valid
14.0ms	16×	body	320	nan
6.0ms	13×	body	160	valid
1.0ms	3×	body	160	nan

simplify1.2s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.4b

localize72.0ms

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))))
0.4b	(* (sqrt 2) t)
13.6b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
20.5b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite154.0ms

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:

58.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
15.0ms	(* (sqrt 2) t)
26.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
53.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

485.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
79.0ms	(* (sqrt 2) t)
264.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify1.0s

Counts

96 → 96

Iterations

Iter	Nodes
done	2014
2	1525
1	458
0	170

prune508.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.0b

localize37.0ms

Local error

Found 4 expressions with local error:

4.0b	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
6.5b	(/ (* l l) x)
7.6b	(/ (* t t) x)
27.9b	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

rewrite94.0ms

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:

34.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
9.0ms	(/ (* l l) x)
9.0ms	(/ (* t t) x)
40.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4))
22.0ms	(/ (* l l) x)
20.0ms	(/ (* t t) x)
350.0ms	(sqrt (+ (* 2 (+ (* t t) (/ (* l l) x))) (* (/ (* t t) x) 4)))

simplify503.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	2000
1	536
0	172

prune568.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
4.0b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
7.6b	(/ (* t t) x)
27.9b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite127.0ms

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:

7.0ms	(* (sqrt 2) t)
27.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
24.0ms	(/ (* t t) x)
68.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sqrt 2) t)
78.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
27.0ms	(/ (* t t) x)
355.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify504.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	2000
1	498
0	171

prune577.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
4.0b	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
7.6b	(/ (* t t) x)
27.9b	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

43.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
28.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
9.0ms	(/ (* t t) x)
50.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
76.0ms	(+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4))
27.0ms	(/ (* t t) x)
299.0ms	(sqrt (+ (* 2 (+ (* t t) (/ l (/ x l)))) (* (/ (* t t) x) 4)))

simplify521.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	2000
1	533
0	176

prune560.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

regimes523.0ms

Accuracy

78.2% (5.1b remaining)

Error of 9.4b against oracle of 4.3b and baseline of 27.8b

bsearch1.4s

Steps

Iters	Range		Point
9	6.304552648946534e+101	1.0488449087684188e+108	9.234874397993673e+103
10	-4.0078265890482388e-174	-2.271177371877917e-185	-5.330429831411802e-184
11	-4.997562010672814e-139	-5.210697667798281e-160	-5.64615525414727e-160
10	-6.1949627884649066e+72	-9.200494817440825e+61	-2.723485209640235e+72

simplify56.0ms

Iterations

Iter	Nodes
done	64
1	64
0	50

end0.0ms

sample9.5s

Algorithm

intervals

Results

2.8s	10352×	body	80	nan
1.8s	5085×	body	80	valid
1.2s	1019×	body	640	valid
1.0s	863×	body	1280	valid
665.0ms	607×	body	1280	nan
521.0ms	616×	body	640	nan
461.0ms	662×	body	320	valid
284.0ms	345×	body	320	nan
135.0ms	371×	body	160	valid
68.0ms	189×	body	160	nan