Details

sample264.0ms

Algorithm

intervals

Results

87.0ms	289×	body	80	nan
20.0ms	171×	body	80	valid
16.0ms	27×	body	1280	valid
13.0ms	23×	body	1280	nan
12.0ms	24×	body	640	valid
10.0ms	22×	body	640	nan
7.0ms	21×	body	320	valid
4.0ms	12×	body	320	nan
3.0ms	7×	body	160	nan
3.0ms	13×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	18	27
1	39	27
2	93	27
3	198	27
4	432	27
5	777	27
6	1367	27
7	3546	27
done	5000	27

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize45.0ms

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)
13.0b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite245.0ms

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:

86.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
20.0ms	(* (sqrt 2.0) t)
62.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
67.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.7s

Counts

4 → 12

Calls

4 calls:

658.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
74.0ms	(* (sqrt 2.0) t)
335.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.6s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.9s

Counts

92 → 92

Iterations

Useful iterations: 2 (502.0ms)

Iter	Nodes	Cost
0	168	2472
1	457	2291
2	2627	2087
done	5000	2087

prune379.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.2b

localize30.0ms

Local error

Found 4 expressions with local error:

2.8b	(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
6.0b	(/ (pow l 2) x)
9.5b	(/ (pow t 2) x)
24.6b	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

rewrite155.0ms

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-+l+` `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:

40.0ms	(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
15.0ms	(/ (pow l 2) x)
16.0ms	(/ (pow t 2) x)
79.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x)))
20.0ms	(/ (pow l 2) x)
31.0ms	(/ (pow t 2) x)
363.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

simplify1.9s

Counts

142 → 142

Iterations

Useful iterations: 2 (626.0ms)

Iter	Nodes	Cost
0	254	2312
1	568	2086
2	2934	1875
done	5000	1875

prune742.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
2.8b	(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x)))
9.5b	(/ (pow t 2) x)
24.6b	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-r/` `add-cbrt-cube` `associate-/l`
7×	`pow1` `sqrt-prod`
6×	`associate-l` `add-log-exp`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`associate-+l+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 103

Calls

4 calls:

20.0ms	(* (sqrt 2.0) t)
61.0ms	(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x)))
18.0ms	(/ (pow t 2) x)
97.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x))))

series565.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sqrt 2.0) t)
88.0ms	(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x)))
37.0ms	(/ (pow t 2) x)
394.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x))))

simplify1.7s

Counts

115 → 115

Iterations

Useful iterations: 2 (528.0ms)

Iter	Nodes	Cost
0	215	1938
1	530	1768
2	2700	1613
done	5001	1613

prune552.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
2.8b	(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x)))
9.5b	(/ (pow t 2) x)
24.6b	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x))))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`add-exp-log`
17×	`pow1`
12×	`unpow-prod-down` `add-cbrt-cube`
8×	`associate-r/` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l`
6×	`add-log-exp`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`associate-+l+`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `pow-exp` `clear-num` `sum-log` `*-commutative` `div-inv`

Counts

4 → 103

Calls

4 calls:

71.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
33.0ms	(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x)))
16.0ms	(/ (pow t 2) x)
64.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x))))

series602.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* (cbrt (sqrt 2.0)) t))
105.0ms	(+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x)))
28.0ms	(/ (pow t 2) x)
398.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ l (/ x l)))) (* 4.0 (/ (pow t 2) x))))

simplify2.3s

Counts

115 → 115

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	223	2181
1	569	1998
2	2812	1667
done	5002	1602

prune609.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.4b

regimes734.0ms

Accuracy

77.5% (5.3b remaining)

Error of 9.2b against oracle of 4.0b and baseline of 27.4b

bsearch289.0ms

Steps

Iters	Range		Point
7	1.432588733015798e+113	5.43248225308003e+114	3.1662692068386204e+113
8	-3.06497223010665e+106	-6.700067088620505e+103	-1.397305156304466e+105

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	91
1	53	91
done	53	91

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.8s	10001×	body	80	nan
1.1s	844×	body	1280	valid
716.0ms	5053×	body	80	valid
478.0ms	1076×	body	640	valid
431.0ms	562×	body	1280	nan
375.0ms	608×	body	640	nan
255.0ms	635×	body	320	valid
190.0ms	336×	body	320	nan
89.0ms	392×	body	160	valid
76.0ms	176×	body	160	nan