Details

sample30.0ms

Algorithm

intervals

Results

15.0ms

431×

body

valid

simplify77.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (12.0ms)

Iter	Nodes	Cost
0	7	15
1	14	14
2	29	11
3	51	8
4	71	8
5	79	8
done	79	8

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

71.0ms	(+ (+ (* x x) (* y y)) (* y y))
188.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series145.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(+ (+ (* x x) (* y y)) (* y y))
72.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify1.5s

Counts

43 → 43

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	60	681
1	209	601
2	1169	453
done	5002	436

prune200.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

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

simplify10.6s

Counts

13 → 13

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	21	140
1	33	137
2	118	121
3	511	121
4	4030	121
done	5000	121

prune39.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.2b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
5.7b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.7b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

48.0ms	(+ (+ (* x x) (* y y)) (* y y))
0.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
36.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
42.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (+ (* x x) (* y y)) (* y y))
186.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
65.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
81.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify801.0ms

Counts

76 → 76

Iterations

Useful iterations: done (798.0ms)

Iter	Nodes	Cost
0	76	1364
1	197	1032
2	997	742
done	5001	645

prune309.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 17

Calls

1 calls:

12.0ms

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

series56.0ms

Counts

1 → 3

Calls

1 calls:

56.0ms

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

simplify4.3s

Counts

20 → 20

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	36	297
1	114	289
2	556	210
3	4830	196
done	5000	196

prune51.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes170.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	9	12
done	9	12

end0.0ms

sample1.3s

Algorithm

intervals

Results

932.0ms

14175×

body

valid