Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	88×	body	1280	valid
11.0ms	42×	body	640	valid
5.0ms	180×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	13×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	27	6
4	51	6
5	118	6
6	453	6
7	3607	6
done	5002	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.7b	(- (exp (* a x)) 1.0)

rewrite47.0ms

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:

9.0ms	(exp (* a x))
36.0ms	(- (exp (* a x)) 1.0)

series67.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
53.0ms	(- (exp (* a x)) 1.0)

simplify2.3s

Counts

46 → 46

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	79	557
1	183	460
2	598	386
3	3356	328
done	5000	325

prune202.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow a 2))
0.1b	(* 1/6 (pow a 3))
11.0b	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
13.8b	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `expm1-log1p-u` `cube-prod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unpow2`
1×	`cube-mult` `unpow3`

Counts

4 → 82

Calls

4 calls:

18.0ms	(* 1/2 (pow a 2))
20.0ms	(* 1/6 (pow a 3))
0.0ms	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
0.0ms	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/2 (pow a 2))
68.0ms	(* 1/6 (pow a 3))
133.0ms	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
136.0ms	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

simplify870.0ms

Counts

94 → 94

Iterations

Useful iterations: done (866.0ms)

Iter	Nodes	Cost
0	137	1036
1	315	960
2	1230	857
done	5001	816

prune425.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (* a a))
1.7b	(* x (+ (* (* 1/2 (* a a)) x) a))
8.1b	(* (* 1/2 (* a a)) x)

rewrite417.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
3×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`associate-*r/` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

3 → 68

Calls

3 calls:

19.0ms	(* 1/2 (* a a))
312.0ms	(* x (+ (* (* 1/2 (* a a)) x) a))
83.0ms	(* (* 1/2 (* a a)) x)

series213.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* 1/2 (* a a))
112.0ms	(* x (+ (* (* 1/2 (* a a)) x) a))
44.0ms	(* (* 1/2 (* a a)) x)

simplify2.2s

Counts

77 → 77

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	106	833
1	325	741
2	2213	655
done	5002	653

prune253.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

regimes252.0ms

Accuracy

96.9% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 21.6b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	18	26
done	18	26

end0.0ms

sample2.1s

Algorithm

intervals

Results

759.0ms	2685×	body	1280	valid
342.0ms	1343×	body	640	valid
329.0ms	5567×	body	80	valid
224.0ms	717×	body	320	valid
34.0ms	411×	body	160	valid