Details

sample169.0ms

Algorithm

intervals

Results

105.0ms	175×	body	1280	valid
17.0ms	50×	body	640	valid
15.0ms	282×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.1s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.3b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite134.0ms

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:

21.0ms	(- (exp x) 2.0)
111.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series141.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(- (exp x) 2.0)
116.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify860.0ms

Counts

41 → 41

Iterations

Useful iterations: done (858.0ms)

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

prune251.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

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:

50.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
19.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
36.0ms	(* 1/360 (pow x 6))
25.0ms	(* 1/12 (pow x 4))

series1.0s

Counts

4 → 12

Calls

4 calls:

584.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
273.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
101.0ms	(* 1/360 (pow x 6))
81.0ms	(* 1/12 (pow x 4))

simplify1.3s

Counts

87 → 87

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	133	1068
1	343	934
2	1423	888
done	5002	879

prune532.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
28.4b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
28.4b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
28.4b	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite392.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

277.0ms	(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
33.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
34.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
42.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

290.0ms	(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
254.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
244.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
259.0ms	(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify1.3s

Counts

107 → 107

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	161	4106
1	384	3755
2	1367	3529
done	5001	3052

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(- 2.0 (exp (- x)))
3.1b	(- (exp x) (- 2.0 (exp (- x))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

18.0ms	(- 2.0 (exp (- x)))
62.0ms	(- (exp x) (- 2.0 (exp (- x))))

series128.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- 2.0 (exp (- x)))
106.0ms	(- (exp x) (- 2.0 (exp (- x))))

simplify3.4s

Counts

39 → 39

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	82	422
1	191	393
2	644	375
3	3911	371
done	5001	371

prune199.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes75.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.4s	5723×	body	1280	valid
867.0ms	8110×	body	80	valid
504.0ms	1258×	body	640	valid
133.0ms	595×	body	320	valid
45.0ms	291×	body	160	valid