Details

sample127.0ms

Algorithm

intervals

Results

89.0ms

606×

body

valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1809
3	551
2	177
1	55
0	19

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 4.0 (fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (fma b b (* a a)) 2.0) 1.0))
0.1b	(* (* b b) (- 1.0 (* 3.0 a)))
0.1b	(fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b	(pow (fma b b (* a a)) 2.0)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `unpow-prod-down` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-*r/` `fma-udef`
1×	`pow-to-exp` `pow-pow` `flip3--` `associate-l` `pow-exp` `*-commutative` `flip--` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

1.0ms	(fma 4.0 (fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (fma b b (* a a)) 2.0) 1.0))
44.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
0.0ms	(fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a))))
4.0ms	(pow (fma b b (* a a)) 2.0)

series427.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(fma 4.0 (fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (fma b b (* a a)) 2.0) 1.0))
59.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
78.0ms	(fma (* a a) (+ a 1.0) (* (* b b) (- 1.0 (* 3.0 a))))
146.0ms	(pow (fma b b (* a a)) 2.0)

simplify1.4s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1309
1	418
0	159

prune652.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize87.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (fma b b (* a a)) 2.0)) (cbrt (pow (fma b b (* a a)) 2.0)))
20.5b	(cbrt (pow (fma b b (* a a)) 2.0))
20.5b	(cbrt (pow (fma b b (* a a)) 2.0))
20.5b	(cbrt (pow (fma b b (* a a)) 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`*-un-lft-identity` `add-cube-cbrt`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

18.0ms	(* (cbrt (pow (fma b b (* a a)) 2.0)) (cbrt (pow (fma b b (* a a)) 2.0)))
2.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
3.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
3.0ms	(cbrt (pow (fma b b (* a a)) 2.0))

series906.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(* (cbrt (pow (fma b b (* a a)) 2.0)) (cbrt (pow (fma b b (* a a)) 2.0)))
216.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
201.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
238.0ms	(cbrt (pow (fma b b (* a a)) 2.0))

simplify3.0s

Counts

129 → 129

Iterations

Iter	Nodes
done	5037
4	3020
3	1066
2	522
1	236
0	122

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize121.0ms

Local error

Found 4 expressions with local error:

13.1b	(sqrt (pow (fma b b (* a a)) 2.0))
13.1b	(sqrt (pow (fma b b (* a a)) 2.0))
20.5b	(cbrt (pow (fma b b (* a a)) 2.0))
20.5b	(cbrt (pow (fma b b (* a a)) 2.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`cbrt-prod` `unpow-prod-down` `sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
6×	`rem-sqrt-square` `sqr-pow`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 76

Calls

4 calls:

3.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
3.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
2.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
2.0ms	(cbrt (pow (fma b b (* a a)) 2.0))

series984.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
219.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
264.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
270.0ms	(cbrt (pow (fma b b (* a a)) 2.0))

simplify2.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5002
4	1693
3	675
2	286
1	143
0	82

prune954.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize107.0ms

Local error

Found 4 expressions with local error:

13.1b	(sqrt (pow (fma b b (* a a)) 2.0))
13.1b	(sqrt (pow (fma b b (* a a)) 2.0))
20.5b	(cbrt (pow (fma b b (* a a)) 2.0))
20.5b	(cbrt (pow (fma b b (* a a)) 2.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`cbrt-prod` `unpow-prod-down` `sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
6×	`rem-sqrt-square` `sqr-pow`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 76

Calls

4 calls:

3.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
3.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
2.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
2.0ms	(cbrt (pow (fma b b (* a a)) 2.0))

series865.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
221.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
235.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
195.0ms	(cbrt (pow (fma b b (* a a)) 2.0))

simplify2.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5002
4	1693
3	675
2	286
1	143
0	82

prune795.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes254.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	17

end0.0ms

sample4.1s

Algorithm

intervals

Results

3.5s

20397×

body

valid