Details

sample15.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
2.0ms	105×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	5	6
1	7	5
done	7	5

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.6b

localize4.0ms

Local error

Found 1 expressions with local error:

21.1b

(sqrt (fma x x y))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
1×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

1.0ms

(sqrt (fma x x y))

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(sqrt (fma x x y))

simplify2.2s

Counts

18 → 18

Iterations

Useful iterations: 5 (962.0ms)

Iter	Nodes	Cost
0	37	145
1	75	127
2	166	120
3	421	118
4	970	117
5	2289	116
done	5000	116

prune55.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
21.1b	(sqrt (+ (* x x) y))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

3.0ms	(+ (* x x) y)
5.0ms	(sqrt (+ (* x x) y))

series66.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (* x x) y)
46.0ms	(sqrt (+ (* x x) y))

simplify3.4s

Counts

38 → 38

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	63	345
1	152	284
2	426	250
3	1291	248
4	4277	247
done	5001	247

prune88.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

21.1b

(sqrt (fma x x y))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
1×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

1.0ms

(sqrt (fma x x y))

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(sqrt (fma x x y))

simplify2.1s

Counts

18 → 18

Iterations

Useful iterations: 5 (937.0ms)

Iter	Nodes	Cost
0	37	145
1	75	127
2	166	120
3	421	118
4	970	117
5	2289	116
done	5000	116

prune43.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma (/ y x) 1/2 x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma (/ y x) 1/2 x)

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(fma (/ y x) 1/2 x)

simplify2.3s

Counts

13 → 13

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	17	110
1	23	107
2	50	95
3	137	95
4	481	95
5	1844	95
done	5001	95

prune23.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 21.2b

bsearch44.0ms

Steps

Iters	Range		Point
6	3.05690573887077e+112	2.2882387430117383e+113	7.4055700216532296e+112
9	-9.454570341338981e+157	-2.2087357092495854e+152	-1.3614720717698548e+154

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
done	14	26

end0.0ms

sample367.0ms

Algorithm

intervals

Results

144.0ms	8000×	body	80	valid
56.0ms	2617×	body	80	nan