Details

sample88.0ms

Algorithm

intervals

Results

28.0ms	73×	body	1280	valid
24.0ms	216×	body	80	valid
9.0ms	35×	body	640	valid
3.0ms	22×	body	320	valid
2.0ms	19×	body	160	valid

simplify7.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5022
8	3043
7	758
6	221
5	94
4	45
3	24
2	16
1	11
0	6

prune69.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize37.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
5.0b	(- (exp (* a x)) 1.0)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
6×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

6.0ms	(exp (* a x))
59.0ms	(- (exp (* a x)) 1.0)

series343.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(exp (* a x))
320.0ms	(- (exp (* a x)) 1.0)

simplify5.4s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
3	1461
2	418
1	182
0	79

prune291.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x a) (* x a))
0.2b	(* (* x a) (* x a))
3.8b	(fma (* (* x a) (* x a)) 1/2 (* x a))
15.6b	(fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
34×	`pow-prod-down`
28×	`add-exp-log` `add-cbrt-cube`
16×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
4×	`add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `pow-plus` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `fma-udef`

Counts

4 → 92

Calls

4 calls:

74.0ms	(* (* x a) (* x a))
58.0ms	(* (* x a) (* x a))
1.0ms	(fma (* (* x a) (* x a)) 1/2 (* x a))
1.0ms	(fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* x a) (* x a))
61.0ms	(* (* x a) (* x a))
110.0ms	(fma (* (* x a) (* x a)) 1/2 (* x a))
220.0ms	(fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a)))

simplify12.5s

Counts

104 → 104

Iterations

Iter	Nodes
done	5014
3	3641
2	650
1	168
0	74

prune807.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* a x) (* a x))
3.8b	(fma (* (* a x) (* a x)) 1/2 (* a x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

41×	`pow1`
17×	`pow-prod-down`
14×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
4×	`pow-sqr` `pow-prod-up`
2×	`add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `pow-plus` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `fma-udef`

Counts

2 → 46

Calls

2 calls:

54.0ms	(* (* a x) (* a x))
1.0ms	(fma (* (* a x) (* a x)) 1/2 (* a x))

series190.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(* (* a x) (* a x))
121.0ms	(fma (* (* a x) (* a x)) 1/2 (* a x))

simplify7.9s

Counts

52 → 52

Iterations

Iter	Nodes
done	5084
3	2302
2	440
1	129
0	54

prune469.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize133.0ms

Local error

Found 4 expressions with local error:

15.6b	(fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a)))
21.5b	(cbrt (fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a))))
21.5b	(cbrt (fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a))))
21.5b	(cbrt (fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a)))
2.0ms	(cbrt (fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a))))
2.0ms	(cbrt (fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a))))
14.0ms	(cbrt (fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a))))

series2.4s

Counts

4 → 12

Calls

4 calls:

184.0ms	(fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a)))
745.0ms	(cbrt (fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a))))
803.0ms	(cbrt (fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a))))
644.0ms	(cbrt (fma (* (* (* x a) (* x a)) (* x a)) 1/6 (fma (* (* x a) (* x a)) 1/2 (* x a))))

simplify9.3s

Counts

61 → 61

Iterations

Iter	Nodes
done	5002
3	2288
2	566
1	215
0	90

prune652.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes636.0ms

Accuracy

97% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 21.2b

bsearch2.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	21
1	21
0	19

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.4s	2733×	body	1280	valid
518.0ms	5387×	body	80	valid
399.0ms	1291×	body	640	valid
118.0ms	748×	body	320	valid
46.0ms	427×	body	160	valid