Details

sample89.0ms

Algorithm

intervals

Results

59.0ms	183×	body	1280	valid
8.0ms	246×	body	80	valid
6.0ms	36×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	12×	body	160	valid

simplify205.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.7b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite87.0ms

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)
73.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series80.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(- (exp x) 2.0)
66.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify85.0ms

Counts: 41 → 41

prune97.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

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))

rewrite69.0ms

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:

10.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
30.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
14.0ms	(* 1/360 (pow x 6))
13.0ms	(* 1/12 (pow x 4))

series307.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
60.0ms	(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
61.0ms	(* 1/360 (pow x 6))
41.0ms	(* 1/12 (pow x 4))

simplify46.0ms

Counts: 87 → 87

prune226.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* 1/12 (pow x 4))
30.9b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
30.9b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-exp-log` `associate-r`
12×	`add-cube-cbrt`
8×	`unpow-prod-down` `sqrt-prod` `add-cbrt-cube`
6×	`pow1` `associate-l` `prod-exp` `unswap-sqr`
4×	`sqrt-div` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

12.0ms	(* 1/12 (pow x 4))
12.0ms	(* 1/12 (pow x 4))
40.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
40.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 1/12 (pow x 4))
40.0ms	(* 1/12 (pow x 4))
112.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
108.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify40.0ms

Counts: 94 → 94

prune331.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
5.7b	(log (exp (sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))))
30.9b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
30.9b	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt` `sqrt-prod`
9×	`add-exp-log`
8×	`log-pow`
7×	`pow1` `exp-prod` `associate-r`
6×	`add-cbrt-cube`
4×	`unpow-prod-down` `sqrt-div` `add-log-exp`
3×	`log-prod` `associate-l` `prod-exp` `distribute-lft-out` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `sqr-pow`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

12.0ms	(* 1/12 (pow x 4))
73.0ms	(log (exp (sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))))
36.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
43.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* 1/12 (pow x 4))
120.0ms	(log (exp (sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))))
109.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
106.0ms	(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify67.0ms

Counts: 88 → 88

prune345.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.4s	5636×	body	1280	valid
378.0ms	8061×	body	80	valid
264.0ms	1231×	body	640	valid
77.0ms	661×	body	320	valid
54.0ms	282×	body	160	valid