Details

sample45.0ms

Algorithm

intervals

Results

27.0ms

482×

body

valid

simplify84.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	7	15
1	14	14
2	29	11
3	50	8
4	68	8
5	74	8
done	74	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 1 expressions with local error:

0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
6×	`sum-log`
3×	`fma-def`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `associate-+l+` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 19

Calls

1 calls:

198.0ms

(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify2.2s

Counts

22 → 22

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	43	392
1	125	319
2	454	258
3	2203	202
done	5001	201

prune92.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 3 (* y y) (* x 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 3 (* y y) (* x x))

series56.0ms

Counts

1 → 3

Calls

1 calls:

56.0ms

(fma 3 (* y y) (* x x))

simplify3.7s

Counts

13 → 13

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	21	140
1	32	137
2	71	121
3	204	121
4	670	121
5	3210	121
done	5000	121

prune50.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
7.8b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
7.8b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 46

Calls

3 calls:

0.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
66.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
42.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series300.0ms

Counts

3 → 9

Calls

3 calls:

188.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
54.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
58.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify1.6s

Counts

55 → 55

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	61	1075
1	133	772
2	385	552
3	1250	452
done	5000	438

prune209.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y (* y 3) (* x x))
0.2b	(* (sqrt (fma y (* y 3) (* x x))) (sqrt (fma y (* y 3) (* x x))))
7.8b	(sqrt (fma y (* y 3) (* x x)))
7.8b	(sqrt (fma y (* y 3) (* x x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 91

Calls

4 calls:

1.0ms	(fma y (* y 3) (* x x))
23.0ms	(* (sqrt (fma y (* y 3) (* x x))) (sqrt (fma y (* y 3) (* x x))))
2.0ms	(sqrt (fma y (* y 3) (* x x)))
2.0ms	(sqrt (fma y (* y 3) (* x x)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma y (* y 3) (* x x))
47.0ms	(* (sqrt (fma y (* y 3) (* x x))) (sqrt (fma y (* y 3) (* x x))))
72.0ms	(sqrt (fma y (* y 3) (* x x)))
79.0ms	(sqrt (fma y (* y 3) (* x x)))

simplify4.9s

Counts

103 → 103

Iterations

Useful iterations: 4 (2.6s)

Iter	Nodes	Cost
0	73	1734
1	119	1171
2	279	1057
3	908	1012
4	3698	980
done	5000	980

prune286.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes223.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	10	15
done	10	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.0s

14191×

body

valid