Details

sample70.0ms

Algorithm

intervals

Results

27.0ms	93×	body	1280	valid
11.0ms	20×	body	320	valid
8.0ms	41×	body	640	valid
7.0ms	176×	body	80	valid
1.0ms	11×	body	160	valid

simplify3.8s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.1b	(- (exp (* a x)) 1.0)

rewrite40.0ms

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:

7.0ms	(exp (* a x))
31.0ms	(- (exp (* a x)) 1.0)

series55.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(exp (* a x))
40.0ms	(- (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

prune156.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow a 2))
0.3b	(* 1/6 (pow a 3))
6.0b	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
13.9b	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

rewrite65.0ms

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:

24.0ms	(* 1/2 (pow a 2))
35.0ms	(* 1/6 (pow a 3))
1.0ms	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
1.0ms	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 1/2 (pow a 2))
52.0ms	(* 1/6 (pow a 3))
138.0ms	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
171.0ms	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

simplify743.0ms

Counts

94 → 94

Iterations

Useful iterations: done (740.0ms)

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

prune374.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 1/6) a)
0.3b	(* x 1/6)
1.0b	(* x (+ (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x) a))
4.6b	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)

rewrite954.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

18.0ms	(* (* x 1/6) a)
8.0ms	(* x 1/6)
725.0ms	(* x (+ (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x) a))
200.0ms	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)

series307.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* x 1/6) a)
26.0ms	(* x 1/6)
146.0ms	(* x (+ (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x) a))
103.0ms	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)

simplify3.3s

Counts

101 → 101

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	158	1401
1	509	1214
2	4052	1083
done	5000	1082

prune464.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* 1/6 x) a 1/2)
0.3b	(* 1/6 x)
2.0b	(* (* x (* (fma (* 1/6 x) a 1/2) (* a a))) x)
4.6b	(* x (* (fma (* 1/6 x) a 1/2) (* a a)))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

0.0ms	(fma (* 1/6 x) a 1/2)
8.0ms	(* 1/6 x)
174.0ms	(* (* x (* (fma (* 1/6 x) a 1/2) (* a a))) x)
63.0ms	(* x (* (fma (* 1/6 x) a 1/2) (* a a)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma (* 1/6 x) a 1/2)
15.0ms	(* 1/6 x)
131.0ms	(* (* x (* (fma (* 1/6 x) a 1/2) (* a a))) x)
146.0ms	(* x (* (fma (* 1/6 x) a 1/2) (* a a)))

simplify2.2s

Counts

91 → 91

Iterations

Useful iterations: 2 (479.0ms)

Iter	Nodes	Cost
0	121	1267
1	336	1193
2	2442	997
done	5004	997

prune327.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes261.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.9b

bsearch2.0ms

simplify15.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	43
1	33	43
2	37	43
3	41	43
done	41	43

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	2712×	body	1280	valid
307.0ms	5455×	body	80	valid
229.0ms	1272×	body	640	valid
173.0ms	779×	body	320	valid
58.0ms	407×	body	160	valid