Details

sample149.0ms

Algorithm

intervals

Results

85.0ms	163×	body	1280	valid
26.0ms	251×	body	80	valid
12.0ms	44×	body	640	valid
5.0ms	28×	body	320	valid
2.0ms	18×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	26	8
3	40	8
4	56	8
5	62	8
6	71	8
7	88	8
8	248	8
9	788	8
10	3132	8
done	5000	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
6.4b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `associate-+l+` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
92.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series99.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(- (exp x) 2.0)
84.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify697.0ms

Counts

41 → 41

Iterations

Useful iterations: done (695.0ms)

Iter	Nodes	Cost
0	93	511
1	215	465
2	832	445
done	5001	433

prune180.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.1b	(* 1/360 (pow x 6))
0.1b	(* 1/12 (pow x 4))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
12×	`*-un-lft-identity`
11×	`add-log-exp`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

11.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
34.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
17.0ms	(* 1/360 (pow x 6))
34.0ms	(* 1/12 (pow x 4))

series408.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
73.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
67.0ms	(* 1/360 (pow x 6))
56.0ms	(* 1/12 (pow x 4))

simplify1.0s

Counts

87 → 87

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	133	1068
1	343	934
2	1413	888
done	5001	879

prune339.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp (- x)) 2.0)
6.1b	(+ (exp x) (- (exp (- x)) 2.0))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `associate-+r+` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

2 → 31

Calls

2 calls:

50.0ms	(- (exp (- x)) 2.0)
68.0ms	(+ (exp x) (- (exp (- x)) 2.0))

series121.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(- (exp (- x)) 2.0)
88.0ms	(+ (exp x) (- (exp (- x)) 2.0))

simplify628.0ms

Counts

37 → 37

Iterations

Useful iterations: 2 (154.0ms)

Iter	Nodes	Cost
0	77	392
1	197	364
2	764	344
done	5001	344

prune109.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
39.6b	(/ (- (pow x 4) (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
55×	`difference-of-squares`
48×	`times-frac`
43×	`*-un-lft-identity`
29×	`add-cube-cbrt`
28×	`unpow-prod-down`
22×	`sqr-pow`
21×	`add-exp-log` `associate-r`
12×	`add-cbrt-cube`
9×	`associate-l` `prod-exp` `unswap-sqr`
8×	`associate-/r*`
7×	`distribute-lft-out--` `unpow2`
6×	`associate-/l*`
4×	`pow1` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 154

Calls

4 calls:

24.0ms	(* 1/12 (pow x 4))
13.0ms	(* 1/12 (pow x 4))
13.0ms	(* 1/12 (pow x 4))
144.0ms	(/ (- (pow x 4) (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* 1/12 (pow x 4))
46.0ms	(* 1/12 (pow x 4))
79.0ms	(* 1/12 (pow x 4))
248.0ms	(/ (- (pow x 4) (* (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (- (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify1.5s

Counts

166 → 166

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	215	6005
1	532	5797
2	2166	5482
done	5000	4898

prune663.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	15
1	17	15
done	17	15

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.5s	5632×	body	1280	valid
484.0ms	310×	body	160	valid
419.0ms	7937×	body	80	valid
384.0ms	1242×	body	640	valid
172.0ms	653×	body	320	valid