Details

sample40.0ms

Algorithm

intervals

Results

14.0ms	81×	body	1280	valid
5.0ms	49×	body	640	valid
4.0ms	177×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	9×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	3255
6	440
5	113
4	49
3	26
2	18
1	11
0	6

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.1b	(- (exp (* a x)) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

3.0ms	(exp (* a x))
9.0ms	(- (exp (* a x)) 1.0)

series64.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(exp (* a x))
47.0ms	(- (exp (* a x)) 1.0)

simplify1.1s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
3	2000
2	389
1	116
0	53

prune151.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.4b

localize36.0ms

Local error

Found 4 expressions with local error:

1.6b	(* x (+ (* (* a a) (* 1/2 x)) a))
7.2b	(* (* a a) (* 1/2 x))
14.1b	(+ (* (* 1/6 (pow a 3)) (pow x 3)) (* x (+ (* (* a a) (* 1/2 x)) a)))
17.1b	(* (* 1/6 (pow a 3)) (pow x 3))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
30×	`prod-exp`
23×	`add-cbrt-cube`
18×	`pow1`
16×	`associate-r`
12×	`cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
7×	`pow-to-exp` `pow-exp`
6×	`add-log-exp`
5×	`associate-l`
3×	`unpow-prod-down` `cube-prod` `*-commutative`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+`
1×	`cube-mult` `+-commutative` `sum-log` `unpow3` `unswap-sqr` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

82.0ms	(* x (+ (* (* a a) (* 1/2 x)) a))
36.0ms	(* (* a a) (* 1/2 x))
34.0ms	(+ (* (* 1/6 (pow a 3)) (pow x 3)) (* x (+ (* (* a a) (* 1/2 x)) a)))
40.0ms	(* (* 1/6 (pow a 3)) (pow x 3))

series402.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* x (+ (* (* a a) (* 1/2 x)) a))
28.0ms	(* (* a a) (* 1/2 x))
187.0ms	(+ (* (* 1/6 (pow a 3)) (pow x 3)) (* x (+ (* (* a a) (* 1/2 x)) a)))
97.0ms	(* (* 1/6 (pow a 3)) (pow x 3))

simplify2.3s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	3555
1	536
0	163

prune502.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 3.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* x x) 1/2)
5.6b	(+ (* (* a a) (* (* x x) 1/2)) (* x a))
15.3b	(* (* a a) (* (* x x) 1/2))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-log-exp`
4×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
2×	`associate-l` `*-commutative`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `unswap-sqr`

Counts

3 → 58

Calls

3 calls:

29.0ms	(* (* x x) 1/2)
57.0ms	(+ (* (* a a) (* (* x x) 1/2)) (* x a))
59.0ms	(* (* a a) (* (* x x) 1/2))

series191.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* (* x x) 1/2)
84.0ms	(+ (* (* a a) (* (* x x) 1/2)) (* x a))
70.0ms	(* (* a a) (* (* x x) 1/2))

simplify1.7s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
2	2424
1	315
0	94

prune199.0ms

Pruning

5 alts after pruning (3 fresh and 2 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

Iter	Nodes
done	0
0	0

prune1.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes278.0ms

Accuracy

96.5% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 21.6b

bsearch1.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

658.0ms	2649×	body	1280	valid
469.0ms	5450×	body	80	valid
311.0ms	1357×	body	640	valid
189.0ms	749×	body	320	valid
29.0ms	403×	body	160	valid