Details

sample96.0ms

Algorithm

intervals

Results

29.0ms	86×	body	1280	valid
20.0ms	64×	body	640	valid
7.0ms	170×	body	80	valid
3.0ms	23×	body	320	valid
0.0ms	5×	body	160	valid

simplify6.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5090
8	2971
7	747
6	218
5	94
4	45
3	24
2	16
1	11
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.0b	(- (exp (* a x)) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
6×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

2 → 42

Calls

2 calls:

5.0ms	(exp (* a x))
18.0ms	(- (exp (* a x)) 1.0)

series111.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(exp (* a x))
76.0ms	(- (exp (* a x)) 1.0)

simplify3.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
3	1453
2	414
1	184
0	81

prune464.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x a) (* (* x a) (* x a)))
0.2b	(* (* x a) (* x a))
0.2b	(* (* x a) (* x a))
10.1b	(fma (* (* x a) (* x a)) 1/2 (fma (* (* x a) (* (* x a) (* x a))) 1/6 (* a x)))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

210×	`pow1`
94×	`pow-prod-down`
69×	`add-cbrt-cube` `add-exp-log`
47×	`prod-exp` `cbrt-unprod`
38×	`pow-prod-up`
16×	`pow-sqr`
8×	`pow-plus`
4×	`pow2` `add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `*-commutative`
2×	`swap-sqr`
1×	`cube-unmult` `fma-udef`

Counts

4 → 151

Calls

4 calls:

191.0ms	(* (* x a) (* (* x a) (* x a)))
47.0ms	(* (* x a) (* x a))
47.0ms	(* (* x a) (* x a))
1.0ms	(fma (* (* x a) (* x a)) 1/2 (fma (* (* x a) (* (* x a) (* x a))) 1/6 (* a x)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (* x a) (* (* x a) (* x a)))
60.0ms	(* (* x a) (* x a))
87.0ms	(* (* x a) (* x a))
208.0ms	(fma (* (* x a) (* x a)) 1/2 (fma (* (* x a) (* (* x a) (* x a))) 1/6 (* a x)))

simplify3.1s

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
2	853
1	243
0	101

prune759.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize100.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.2b	(* x (fma 2 a a))
2.0b	(- (exp (* x (fma 2 a a))) (* 1.0 (* 1.0 1.0)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `fma-udef`
5×	`fma-neg` `prod-diff`
4×	`expm1-log1p-u` `exp-sum` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l`
2×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

11.0ms	(exp (* a x))
8.0ms	(exp (* a x))
9.0ms	(* x (fma 2 a a))
31.0ms	(- (exp (* x (fma 2 a a))) (* 1.0 (* 1.0 1.0)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(exp (* a x))
28.0ms	(exp (* a x))
56.0ms	(* x (fma 2 a a))
110.0ms	(- (exp (* x (fma 2 a a))) (* 1.0 (* 1.0 1.0)))

simplify5.8s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	3460
2	738
1	262
0	113

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize155.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.2b	(* x (fma 2 a a))
2.0b	(- (exp (* x (fma 2 a a))) (* 1.0 (* 1.0 1.0)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `fma-udef`
5×	`fma-neg` `prod-diff`
4×	`expm1-log1p-u` `exp-sum` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l`
2×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

12.0ms	(exp (* a x))
11.0ms	(exp (* a x))
20.0ms	(* x (fma 2 a a))
50.0ms	(- (exp (* x (fma 2 a a))) (* 1.0 (* 1.0 1.0)))

series200.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(exp (* a x))
35.0ms	(exp (* a x))
58.0ms	(* x (fma 2 a a))
84.0ms	(- (exp (* x (fma 2 a a))) (* 1.0 (* 1.0 1.0)))

simplify5.7s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	3460
2	738
1	262
0	113

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes701.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.0b

bsearch3.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2692×	body	1280	valid
320.0ms	1363×	body	640	valid
203.0ms	5568×	body	80	valid
81.0ms	777×	body	320	valid
27.0ms	376×	body	160	valid