Details

sample88.0ms

Algorithm

intervals

Results

17.0ms	358×	body	80	nan
8.0ms	32×	body	1280	valid
8.0ms	155×	body	80	valid
7.0ms	38×	body	640	valid
4.0ms	20×	body	640	nan
3.0ms	15×	body	1280	nan
3.0ms	23×	body	320	valid
2.0ms	12×	body	320	nan
1.0ms	8×	body	160	valid
0.0ms	3×	body	160	nan

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	39	14
1	93	14
2	193	14
3	414	14
4	718	14
5	1192	14
6	2816	14
7	5001	14
done	5001	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.9b

localize19.0ms

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)
15.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.1b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite146.0ms

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:

55.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms	(* (sqrt 2.0) t)
29.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
49.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

436.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
41.0ms	(* (sqrt 2.0) t)
225.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify60.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	417	1207
1	2051	1099
2	5002	1094
done	5002	1094

prune296.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.4b

localize17.0ms

Local error

Found 4 expressions with local error:

3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.4b	(/ (pow l 2) x)
11.1b	(/ (pow t 2) x)
31.8b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite58.0ms

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-+r+` `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:

18.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
8.0ms	(/ (pow l 2) x)
8.0ms	(/ (pow t 2) x)
19.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
20.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
166.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify62.0ms

Counts

142 → 142

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	526	1067
1	2113	984
2	5001	978
done	5001	978

prune433.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
11.1b	(/ (pow t 2) x)
31.8b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

14.0ms	(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
17.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
8.0ms	(/ (pow t 2) x)
17.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

series248.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
55.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
19.0ms	(/ (pow t 2) x)
146.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

simplify61.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	493	1099
1	2141	999
2	5001	996
done	5001	996

prune364.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
3.6b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
11.1b	(/ (pow t 2) x)
31.8b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

15.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
18.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
8.0ms	(/ (pow t 2) x)
17.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series341.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
85.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
19.0ms	(/ (pow t 2) x)
182.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify60.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	463	1308
1	1965	1213
2	5001	1210
done	5001	1210

prune343.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.2b

regimes379.0ms

Accuracy

78.3% (5.2b remaining)

Error of 9.1b against oracle of 3.9b and baseline of 27.6b

bsearch478.0ms

Steps

Iters	Range		Point
10	4.037166448428983e+35	2.944857922176075e+52	2.1130028073347647e+52
9	-4.462648400956333e-209	-5.955989317188973e-215	-3.303971389439813e-212
9	-9.870747104696548e-169	-9.533804063462273e-175	-2.203593120725198e-171
7	-8.928275251414201e+148	-2.544246119565285e+147	-1.8290478461764168e+148

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	96
1	67	96
done	67	96

end0.0ms

sample2.2s

Algorithm

intervals

Results

484.0ms	9818×	body	80	nan
261.0ms	5116×	body	80	valid
211.0ms	860×	body	1280	valid
206.0ms	1051×	body	640	valid
141.0ms	582×	body	1280	nan
106.0ms	575×	body	640	nan
89.0ms	635×	body	320	valid
45.0ms	337×	body	320	nan
33.0ms	338×	body	160	valid
15.0ms	169×	body	160	nan