Details

sample90.0ms

Algorithm

intervals

Results

19.0ms	375×	body	80	nan
17.0ms	33×	body	1280	valid
9.0ms	167×	body	80	valid
6.0ms	28×	body	640	valid
5.0ms	21×	body	1280	nan
3.0ms	14×	body	640	nan
2.0ms	16×	body	320	nan
2.0ms	12×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	7×	body	160	nan

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	27
1	39	27
2	86	27
3	177	27
4	344	27
5	550	27
6	899	27
7	1592	27
8	3229	27
done	5001	27

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize18.0ms

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)
14.8b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.6b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite74.0ms

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:

25.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
13.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
28.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

417.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
39.0ms	(* (sqrt 2.0) t)
209.0ms	(- (* (/ (+ 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)))

simplify593.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (142.0ms)

Iter	Nodes	Cost
0	168	2472
1	416	2283
2	1675	2085
done	5001	2085

prune297.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.7b

localize18.0ms

Local error

Found 4 expressions with local error:

3.8b	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
6.9b	(/ (pow l 2) x)
9.7b	(/ (pow t 2) x)
27.2b	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 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`
9×	`add-log-exp`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
3×	`sum-log` `sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `sqrt-div` `pow-exp` `clear-num` `flip-+` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `associate-+r+` `sqrt-pow1` `pow1/2`

Counts

4 → 126

Calls

4 calls:

16.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
6.0ms	(/ (pow l 2) x)
4.0ms	(/ (pow t 2) x)
28.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow l 2) x)
19.0ms	(/ (pow t 2) x)
258.0ms	(sqrt (+ (* 2.0 (pow t 2)) (+ (* 2.0 (/ (pow l 2) x)) (* 4.0 (/ (pow t 2) x)))))

simplify585.0ms

Counts

138 → 138

Iterations

Useful iterations: 2 (191.0ms)

Iter	Nodes	Cost
0	229	2129
1	453	1871
2	1722	1692
done	5000	1692

prune462.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize21.0ms

Local error

Found 4 expressions with local error:

9.7b	(/ (pow t 2) x)
9.7b	(/ (pow t 2) x)
27.2b	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))
27.2b	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`sqrt-div` `associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`pow1` `div-exp` `associate-/r*` `sqrt-prod`
4×	`flip3-+` `frac-add` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv`

Counts

4 → 132

Calls

4 calls:

4.0ms	(/ (pow t 2) x)
5.0ms	(/ (pow t 2) x)
23.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))
26.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow t 2) x)
23.0ms	(/ (pow t 2) x)
258.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))
257.0ms	(sqrt (+ (* 2.0 (+ (* t t) (/ (pow l 2) x))) (* 4.0 (/ (pow t 2) x))))

simplify576.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (162.0ms)

Iter	Nodes	Cost
0	171	2390
1	387	2132
2	1374	1936
done	5001	1936

prune619.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2.0) t)
1.0b	(pow (sqrt 2.0) 3)
11.3b	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
11.3b	(/ t (* (sqrt 2.0) (pow x 2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`div-exp`
13×	`prod-exp`
10×	`sqrt-prod`
8×	`pow1` `pow-to-exp` `pow-exp`
6×	`unpow-prod-down` `times-frac` `cube-prod` `associate-l` `associate-/l*`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`
1×	`cube-mult` `sqrt-pow1` `pow1/2` `unpow3` `pow-prod-down` `*-commutative` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
2.0ms	(pow (sqrt 2.0) 3)
6.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
5.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

series282.0ms

Counts

4 → 10

Calls

4 calls:

38.0ms	(* (sqrt 2.0) t)
0.0ms	(pow (sqrt 2.0) 3)
163.0ms	(/ t (* (pow (sqrt 2.0) 3) (pow x 2)))
80.0ms	(/ t (* (sqrt 2.0) (pow x 2)))

simplify736.0ms

Counts

116 → 116

Iterations

Useful iterations: 2 (189.0ms)

Iter	Nodes	Cost
0	151	1172
1	388	1019
2	1960	938
done	5000	938

prune274.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.1b

regimes496.0ms

Accuracy

66.3% (9.1b remaining)

Error of 12.9b against oracle of 3.9b and baseline of 30.8b

bsearch170.0ms

Steps

Iters	Range		Point
9	5.514934322013309e+56	2.9513659930621936e+63	5.60070758315032e+56
4	-7.071793886822642e-265	-4.409591838871608e-265	-6.971334801643659e-265

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	115
1	56	115
done	56	115

end0.0ms

sample2.1s

Algorithm

intervals

Results

494.0ms	9913×	body	80	nan
266.0ms	5098×	body	80	valid
213.0ms	1032×	body	640	valid
212.0ms	828×	body	1280	valid
145.0ms	581×	body	1280	nan
119.0ms	614×	body	640	nan
105.0ms	666×	body	320	valid
50.0ms	350×	body	320	nan
38.0ms	376×	body	160	valid
17.0ms	178×	body	160	nan