Details

sample42.0ms

Algorithm

intervals

Results

19.0ms	92×	body	1280	valid
5.0ms	44×	body	640	valid
5.0ms	191×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.7b	(- (exp x) 1.0)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

26.0ms	(/ (- (exp x) 1.0) x)
22.0ms	(- (exp x) 1.0)

series62.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- (exp x) 1.0) x)
17.0ms	(- (exp x) 1.0)

simplify70.0ms

Counts: 58 → 58

prune130.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
0.2b	(* 1/6 (pow x 2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log` `add-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp` `sum-log`
2×	`pow1` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 40

Calls

2 calls:

28.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
13.0ms	(* 1/6 (pow x 2))

series52.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1))
30.0ms	(* 1/6 (pow x 2))

simplify31.0ms

Counts: 46 → 46

prune95.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/6 (pow x 2))
0.2b	(* 1/6 (pow x 2))
10.8b	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
10.8b	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
16×	`associate-r`
14×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
6×	`pow1` `associate-l` `prod-exp` `sqrt-prod`
4×	`sqrt-div` `unpow2` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 84

Calls

4 calls:

15.0ms	(* 1/6 (pow x 2))
13.0ms	(* 1/6 (pow x 2))
36.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
38.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

series184.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 1/6 (pow x 2))
27.0ms	(* 1/6 (pow x 2))
67.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
61.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

simplify37.0ms

Counts: 96 → 96

prune270.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

10.8b	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
10.8b	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
10.8b	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
10.8b	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

37.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
36.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
37.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
35.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
65.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
67.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))
63.0ms	(sqrt (+ (* 1/6 (pow x 2)) (+ (* 1/2 x) 1)))

simplify125.0ms

Counts: 72 → 72

prune278.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes60.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.2b

bsearch17.0ms

Steps

Iters	Range		Point
5	-0.00044970739729878565	-0.00011609448734148344	-0.00016561991584697298

simplify1.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

798.0ms	2283×	body	1280	valid
296.0ms	1635×	body	640	valid
162.0ms	5522×	body	80	valid
70.0ms	833×	body	320	valid
24.0ms	431×	body	160	valid