Details

sample33.0ms

Algorithm

intervals

Results

14.0ms	87×	body	1280	valid
4.0ms	43×	body	640	valid
4.0ms	176×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	16×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	27	6
4	51	6
5	110	6
6	272	6
7	1155	6
8	4059	6
done	5000	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.8b	(- (exp (* a x)) 1.0)

rewrite7.0ms

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:

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

series46.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
34.0ms	(- (exp (* a x)) 1.0)

simplify1.6s

Counts

46 → 46

Iterations

Useful iterations: 3 (263.0ms)

Iter	Nodes	Cost
0	79	557
1	180	457
2	559	377
3	2611	328
done	5001	328

prune91.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 6.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (pow a 3))
4.8b	(* (* 1/6 (pow a 3)) x)
9.1b	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
15.4b	(* (* x x) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
18×	`add-sqr-sqrt` `associate-r`
16×	`add-cbrt-cube`
13×	`prod-exp`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-unprod`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `pow-prod-down` `log1p-expm1-u`
3×	`*-commutative`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `fma-def` `distribute-lft-in` `unpow3` `sum-log`

Counts

4 → 93

Calls

4 calls:

7.0ms	(* 1/6 (pow a 3))
12.0ms	(* (* 1/6 (pow a 3)) x)
9.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
40.0ms	(* (* x x) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

series249.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 1/6 (pow a 3))
26.0ms	(* (* 1/6 (pow a 3)) x)
63.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
122.0ms	(* (* x x) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

simplify1.1s

Counts

105 → 105

Iterations

Useful iterations: 2 (174.0ms)

Iter	Nodes	Cost
0	144	1482
1	420	1301
2	2230	1147
done	5001	1147

prune290.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 3.8b

localize15.0ms

Local error

Found 4 expressions with local error:

9.1b	(fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x))
9.1b	(fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x))
23.7b	(sqrt (fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x)))
23.7b	(sqrt (fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 50

Calls

4 calls:

0.0ms	(fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x))
0.0ms	(fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x))
1.0ms	(sqrt (fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x)))
1.0ms	(sqrt (fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x))
60.0ms	(fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x))
113.0ms	(sqrt (fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x)))
117.0ms	(sqrt (fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x)))

simplify960.0ms

Counts

62 → 62

Iterations

Useful iterations: 3 (187.0ms)

Iter	Nodes	Cost
0	64	1036
1	135	956
2	456	884
3	2463	872
done	5001	872

prune239.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 3.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* a x))
3.8b	(log (exp (- (exp (* a x)) 1.0)))
3.8b	(- (exp (* a x)) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

1.0ms	(exp (* a x))
12.0ms	(log (exp (- (exp (* a x)) 1.0)))
5.0ms	(- (exp (* a x)) 1.0)

series88.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(exp (* a x))
35.0ms	(log (exp (- (exp (* a x)) 1.0)))
41.0ms	(- (exp (* a x)) 1.0)

simplify1.8s

Counts

80 → 80

Iterations

Useful iterations: 3 (382.0ms)

Iter	Nodes	Cost
0	132	1134
1	246	864
2	675	702
3	2862	604
done	5001	604

prune164.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 3.8b

regimes125.0ms

Accuracy

96.7% (0.7b remaining)

Error of 5.1b against oracle of 4.4b and baseline of 26.6b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	23	48
1	27	48
done	27	48

end0.0ms

sample973.0ms

Algorithm

intervals

Results

442.0ms	2689×	body	1280	valid
136.0ms	1271×	body	640	valid
126.0ms	5525×	body	80	valid
54.0ms	760×	body	320	valid
21.0ms	433×	body	160	valid