Details

sample422.0ms

Algorithm

intervals

Results

74.0ms	330×	body	80	nan
73.0ms	27×	body	1280	valid
40.0ms	176×	body	80	valid
21.0ms	25×	body	640	valid
19.0ms	18×	body	1280	nan
17.0ms	20×	body	640	nan
10.0ms	17×	body	320	nan
10.0ms	17×	body	320	valid
5.0ms	11×	body	160	valid
3.0ms	6×	body	160	nan

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4592
5	1370
4	472
3	215
2	101
1	44
0	18

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.3b

localize88.0ms

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)
11.6b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
21.1b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite10.0s

Algorithm

rewrite-expression-head

Rules

2006×	`add-sqr-sqrt`
1306×	`*-un-lft-identity`
990×	`associate-l`
959×	`times-frac`
720×	`prod-diff`
610×	`add-cube-cbrt`
504×	`sqrt-prod`
413×	`difference-of-squares`
381×	`unswap-sqr`
337×	`associate-r`
201×	`swap-sqr`
176×	`distribute-lft-out`
148×	`*-commutative`
140×	`distribute-lft-out--`
64×	`difference-of-sqr-1`
48×	`fma-neg`
34×	`associate-/r/`
25×	`associate-/r*`
19×	`flip3--` `flip--`
17×	`div-inv`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `associate--l+` `insert-posit16` `log1p-expm1-u`
2×	`distribute-rgt-in` `cbrt-undiv` `+-commutative` `distribute-lft-in` `div-exp` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down`

Counts

4 → 1328

Calls

4 calls:

2.7s	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
17.0ms	(* (sqrt 2) t)
3.8s	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
3.3s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

483.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
57.0ms	(* (sqrt 2) t)
284.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.4s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify2.5s

Counts

1340 → 1340

Iterations

Iter	Nodes
done	5001
1	2370
0	1048

prune3.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.6b

localize35.0ms

Local error

Found 4 expressions with local error:

4.0b	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (/ (* l l) x))))
5.5b	(/ (* l l) x)
9.5b	(/ (* t t) x)
25.8b	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (/ (* l l) x)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
90×	`times-frac`
77×	`*-un-lft-identity` `add-cube-cbrt`
30×	`associate-/l*`
24×	`swap-sqr` `associate-r` `associate-l`
14×	`add-cbrt-cube` `add-exp-log`
8×	`*-commutative` `unswap-sqr`
6×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 187

Calls

4 calls:

1.0ms	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (/ (* l l) x))))
25.0ms	(/ (* l l) x)
25.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (/ (* l l) x)))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (/ (* l l) x))))
40.0ms	(/ (* l l) x)
37.0ms	(/ (* t t) x)
256.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (/ (* l l) x)))))

simplify1.9s

Counts

199 → 199

Iterations

Iter	Nodes
done	5001
2	2113
1	689
0	279

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
4.0b	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x)))))
9.5b	(/ (* t t) x)
25.8b	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
45×	`times-frac`
44×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-l`
15×	`associate-r` `associate-/l*`
12×	`swap-sqr`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
5×	`*-commutative`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `fma-udef` `div-inv`

Counts

4 → 132

Calls

4 calls:

17.0ms	(* (sqrt 2) t)
1.0ms	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x)))))
36.0ms	(/ (* t t) x)
3.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x))))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sqrt 2) t)
91.0ms	(fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x)))))
43.0ms	(/ (* t t) x)
204.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x))))))

simplify1.4s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1400
1	487
0	205

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize64.0ms

Local error

Found 4 expressions with local error:

9.5b	(/ (* t t) x)
9.5b	(/ (* t t) x)
25.8b	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x))))))
25.8b	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x))))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
90×	`times-frac`
78×	`*-un-lft-identity` `add-cube-cbrt`
30×	`associate-/l*`
24×	`swap-sqr` `associate-r` `associate-l`
14×	`add-cbrt-cube` `add-exp-log`
8×	`*-commutative` `unswap-sqr`
6×	`pow1` `associate-/r*` `sqrt-prod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 192

Calls

4 calls:

27.0ms	(/ (* t t) x)
26.0ms	(/ (* t t) x)
2.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x))))))
3.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x))))))

series550.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (* t t) x)
36.0ms	(/ (* t t) x)
221.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x))))))
253.0ms	(sqrt (fma (* t t) 2 (fma 4 (/ (* t t) x) (* 2 (* l (/ l x))))))

simplify2.5s

Counts

204 → 204

Iterations

Iter	Nodes
done	5026
3	4397
2	1101
1	386
0	163

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

regimes560.0ms

Accuracy

77.4% (5.3b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 27.4b

bsearch465.0ms

Steps

Iters	Range		Point
8	1.1851330097179606e+57	4.62892497053394e+59	4.561118037024944e+59
8	-1.088440472853674e+104	-3.1005758900961096e+100	-1.6626777853889492e+102

simplify18.0ms

Iterations

Iter	Nodes
done	46
1	46
0	40

end0.0ms

sample7.6s

Algorithm

intervals

Results

2.5s	10190×	body	80	nan
1.3s	5134×	body	80	valid
794.0ms	878×	body	1280	valid
703.0ms	981×	body	640	valid
558.0ms	574×	body	1280	nan
477.0ms	562×	body	640	nan
338.0ms	665×	body	320	valid
197.0ms	363×	body	320	nan
115.0ms	342×	body	160	valid
59.0ms	194×	body	160	nan