Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

452×

body

valid

simplify43.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (11.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

10.0ms	(+ (* x x) (* y y))
131.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series68.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* x x) (* y y))
38.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify1.7s

Counts

39 → 39

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	60	574
1	191	470
2	684	382
3	2757	326
done	5000	325

prune98.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(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))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

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

simplify2.5s

Counts

13 → 13

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	21	140
1	32	137
2	70	121
3	203	121
4	668	121
5	3194	121
done	5000	121

prune40.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.2b	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
5.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
5.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

8.0ms	(+ (* x x) (* y y))
0.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
35.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
37.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* x x) (* y y))
133.0ms	(fma (sqrt (+ (+ (* x x) (* y y)) (* y y))) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
53.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))
55.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify1.2s

Counts

72 → 72

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	81	1257
1	199	911
2	582	676
3	1708	576
done	5000	562

prune236.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (* (sqrt 2) y) x)
0.2b	(fma (* 1 (hypot (* (sqrt 2) y) x)) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
0.5b	(* (sqrt 2) y)
5.9b	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `sqrt-prod`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`sqrt-div` `unswap-sqr`
1×	`rem-sqrt-square` `hypot-udef` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `hypot-def`

Counts

4 → 62

Calls

4 calls:

0.0ms	(hypot (* (sqrt 2) y) x)
0.0ms	(fma (* 1 (hypot (* (sqrt 2) y) x)) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
10.0ms	(* (sqrt 2) y)
35.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(hypot (* (sqrt 2) y) x)
261.0ms	(fma (* 1 (hypot (* (sqrt 2) y) x)) (sqrt (+ (+ (* x x) (* y y)) (* y y))) (* y y))
40.0ms	(* (sqrt 2) y)
57.0ms	(sqrt (+ (+ (* x x) (* y y)) (* y y)))

simplify2.2s

Counts

74 → 74

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	108	980
1	217	846
2	626	692
3	2720	525
done	5000	523

prune222.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes110.0ms

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	6	8
1	7	8
done	7	8

end0.0ms

sample614.0ms

Algorithm

intervals

Results

309.0ms

14125×

body

valid