Details

sample49.0ms

Algorithm

intervals

Results

23.0ms

413×

body

valid

simplify78.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	8	15
1	16	14
2	33	11
3	56	8
4	74	8
5	80	8
done	80	8

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

18.0ms	(+ (* x y) (* z z))
50.0ms	(+ (+ (* x y) (* z z)) (* z z))
144.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series182.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* x y) (* z z))
80.0ms	(+ (+ (* x y) (* z z)) (* z z))
62.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify3.2s

Counts

60 → 60

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	76	863
1	228	666
2	839	590
3	3573	521
done	5000	521

prune224.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

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:

1.0ms

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

series59.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

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

simplify3.9s

Counts

13 → 13

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	21	140
1	33	137
2	69	121
3	207	121
4	706	121
5	3689	121
done	5000	121

prune36.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x y) (* z z)) (* z z))
0.3b	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
2.1b	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
2.1b	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

rewrite133.0ms

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:

40.0ms	(+ (+ (* x y) (* z z)) (* z z))
0.0ms	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
52.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
39.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

series621.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(+ (+ (* x y) (* z z)) (* z z))
273.0ms	(fma (sqrt (+ (+ (* x y) (* z z)) (* z z))) (sqrt (+ (+ (* x y) (* z z)) (* z z))) (* z z))
154.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))
128.0ms	(sqrt (+ (+ (* x y) (* z z)) (* z z)))

simplify2.2s

Counts

76 → 76

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	85	1406
1	205	945
2	656	793
3	2755	740
done	5000	737

prune431.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 3 (* z z) (* x y))
0.3b	(* (sqrt (fma 3 (* z z) (* x y))) (sqrt (fma 3 (* z z) (* x y))))
2.0b	(sqrt (fma 3 (* z z) (* x y)))
2.0b	(sqrt (fma 3 (* z z) (* x y)))

rewrite31.0ms

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:

0.0ms	(fma 3 (* z z) (* x y))
22.0ms	(* (sqrt (fma 3 (* z z) (* x y))) (sqrt (fma 3 (* z z) (* x y))))
3.0ms	(sqrt (fma 3 (* z z) (* x y)))
3.0ms	(sqrt (fma 3 (* z z) (* x y)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma 3 (* z z) (* x y))
73.0ms	(* (sqrt (fma 3 (* z z) (* x y))) (sqrt (fma 3 (* z z) (* x y))))
166.0ms	(sqrt (fma 3 (* z z) (* x y)))
165.0ms	(sqrt (fma 3 (* z z) (* x y)))

simplify4.8s

Counts

103 → 103

Iterations

Useful iterations: 4 (2.5s)

Iter	Nodes	Cost
0	76	1776
1	131	1211
2	349	1097
3	1222	1052
4	4490	1020
done	5000	1020

prune298.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes206.0ms

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	8	15
1	12	15
done	12	15

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s

12223×

body

valid