Details

sample85.0ms

Algorithm

intervals

Results

15.0ms	315×	body	80	nan
9.0ms	168×	body	80	valid
7.0ms	36×	body	640	valid
6.0ms	23×	body	1280	valid
5.0ms	20×	body	1280	nan
4.0ms	22×	body	640	nan
2.0ms	14×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	9×	body	320	nan
1.0ms	6×	body	160	nan

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	18	27
1	41	26
2	94	26
3	218	26
4	436	26
5	824	26
6	1335	26
7	2447	26
done	5000	26

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

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))))
0.5b	(* (sqrt 2.0) t)
15.0b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite75.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

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

series1.9s

Counts

4 → 12

Calls

4 calls:

426.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
45.0ms	(* (sqrt 2.0) t)
220.0ms	(- (* (/ (+ 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)))

simplify720.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (166.0ms)

Iter	Nodes	Cost
0	179	2660
1	455	2371
2	2032	2177
done	5001	2177

prune400.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.1b

localize19.0ms

Local error

Found 4 expressions with local error:

5.6b	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
6.9b	(/ (pow t 2) x)
6.9b	(/ (pow l 2) x)
27.7b	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite15.0ms

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×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
4.0ms	(/ (pow l 2) x)
1.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
19.0ms	(/ (pow t 2) x)
19.0ms	(/ (pow l 2) x)
273.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify616.0ms

Counts

139 → 139

Iterations

Useful iterations: 2 (143.0ms)

Iter	Nodes	Cost
0	218	1816
1	382	1665
2	1414	1462
done	5000	1462

prune536.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt 2.0) t)
5.6b	(fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
6.9b	(/ (pow t 2) x)
27.7b	(sqrt (fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

rewrite14.0ms

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×	`add-cbrt-cube` `associate-/l*`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-r` `associate-/r*`
2×	`unswap-sqr`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 100

Calls

4 calls:

5.0ms	(* (sqrt 2.0) t)
0.0ms	(fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sqrt 2.0) t)
71.0ms	(fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x))))
19.0ms	(/ (pow t 2) x)
269.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* l (/ l x)) (* 4.0 (/ (pow t 2) x)))))

simplify574.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (121.0ms)

Iter	Nodes	Cost
0	176	1440
1	327	1325
2	1224	1185
done	5000	1185

prune417.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
5.6b	(fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
6.9b	(/ (pow t 2) x)
27.7b	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`cbrt-prod` `div-exp` `associate-/r*` `sqrt-prod`
1×	`cbrt-undiv` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 89

Calls

4 calls:

1.0ms	(cbrt x)
0.0ms	(fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt x)
86.0ms	(fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x))))
18.0ms	(/ (pow t 2) x)
293.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))) (* 4.0 (/ (pow t 2) x)))))

simplify520.0ms

Counts

101 → 101

Iterations

Useful iterations: done (517.0ms)

Iter	Nodes	Cost
0	170	1556
1	312	1435
2	1145	1222
done	5000	1172

prune435.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

regimes352.0ms

Accuracy

75.7% (5.9b remaining)

Error of 9.8b against oracle of 3.8b and baseline of 28.2b

bsearch509.0ms

Steps

Iters	Range		Point
9	8249416806277068.0	6.908956904862703e+24	6.769189022626266e+24
9	-5.149414502062706e-287	-6.479421214823862e-296	-5.07338813022938e-287
9	-1.9154334448410318e-177	-2.122947083583308e-184	-2.1093237783967825e-178
10	-8.385336723204237e+89	-7.10480317732965e+72	-3.67406841218316e+85

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	171
1	60	171
done	60	171

end0.0ms

sample2.1s

Algorithm

intervals

Results

499.0ms	10142×	body	80	nan
262.0ms	5082×	body	80	valid
237.0ms	879×	body	1280	valid
195.0ms	994×	body	640	valid
142.0ms	587×	body	1280	nan
116.0ms	590×	body	640	nan
97.0ms	649×	body	320	valid
44.0ms	316×	body	320	nan
41.0ms	396×	body	160	valid
22.0ms	217×	body	160	nan