Details

sample130.0ms

Algorithm

intervals

Results

54.0ms	238×	body	160	nan
37.0ms	565×	body	80	nan
20.0ms	256×	body	80	valid

simplify5.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	3499
7	1307
6	580
5	196
4	68
3	37
2	21
1	17
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (fma x x -1)))
31.2b	(sqrt (fma x x -1))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
5×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1` `fma-def` `sqrt-prod`
2×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`

Counts

2 → 34

Calls

2 calls:

5.0ms	(+ x (sqrt (fma x x -1)))
1.0ms	(sqrt (fma x x -1))

series127.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(+ x (sqrt (fma x x -1)))
60.0ms	(sqrt (fma x x -1))

simplify3.1s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
4	4052
3	1250
2	461
1	172
0	73

prune214.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2 x (/ -1/2 x))
0.0b	(+ (fma 2 x (/ -1/2 x)) (/ -1/8 (* x (* x x))))
0.1b	(* x (* x x))
0.2b	(/ -1/8 (* x (* x x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `times-frac` `div-exp` `associate-l` `pow-prod-down` `associate-/l*`
2×	`fma-udef`
1×	`pow2` `+-commutative` `associate-+l+` `clear-num` `associate-/r` `sum-log` `frac-2neg` `flip3-+` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma 2 x (/ -1/2 x))
29.0ms	(+ (fma 2 x (/ -1/2 x)) (/ -1/8 (* x (* x x))))
17.0ms	(* x (* x x))
13.0ms	(/ -1/8 (* x (* x x)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(fma 2 x (/ -1/2 x))
47.0ms	(+ (fma 2 x (/ -1/2 x)) (/ -1/8 (* x (* x x))))
64.0ms	(* x (* x x))
53.0ms	(/ -1/8 (* x (* x x)))

simplify1.2s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	914
1	264
0	119

prune383.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (fma x x -1)))
0.5b	(* (sqrt (sqrt (fma x x -1))) (sqrt (sqrt (fma x x -1))))
31.2b	(sqrt (fma x x -1))
31.2b	(sqrt (fma x x -1))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
31×	`pow1`
20×	`*-un-lft-identity` `pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 132

Calls

4 calls:

4.0ms	(sqrt (sqrt (fma x x -1)))
24.0ms	(* (sqrt (sqrt (fma x x -1))) (sqrt (sqrt (fma x x -1))))
2.0ms	(sqrt (fma x x -1))
3.0ms	(sqrt (fma x x -1))

series330.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(sqrt (sqrt (fma x x -1)))
61.0ms	(* (sqrt (sqrt (fma x x -1))) (sqrt (sqrt (fma x x -1))))
78.0ms	(sqrt (fma x x -1))
75.0ms	(sqrt (fma x x -1))

simplify3.0s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
4	4906
3	1631
2	626
1	289
0	137

prune434.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	16814×	body	80	nan
1.5s	7741×	body	160	nan
734.0ms	8000×	body	80	valid