Details

sample53.0ms

Algorithm

intervals

Results

18.0ms	62×	body	1280	valid
12.0ms	67×	body	640	valid
6.0ms	177×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	15×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.8b	(- (exp x) 1.0)

rewrite52.0ms

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:

35.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

series58.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- (exp x) 1.0) x)
17.0ms	(- (exp x) 1.0)

simplify2.0s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	99	596
1	221	572
2	503	542
3	1095	537
4	2836	536
done	5001	536

prune153.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*` `add-cbrt-cube`
2×	`associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

2 → 40

Calls

2 calls:

26.0ms	(* x (+ 1/2 (* 1/6 x)))
12.0ms	(* 1/6 x)

series89.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(* x (+ 1/2 (* 1/6 x)))
23.0ms	(* 1/6 x)

simplify1.9s

Counts

46 → 46

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	70	356
1	184	328
2	522	298
3	1711	298
done	5000	298

prune76.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
4.5b	(- (/ (exp x) x) (/ 1.0 x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

7.0ms	(/ (exp x) x)
33.0ms	(- (/ (exp x) x) (/ 1.0 x))

series78.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (exp x) x)
51.0ms	(- (/ (exp x) x) (/ 1.0 x))

simplify2.0s

Counts

56 → 56

Iterations

Useful iterations: 4 (817.0ms)

Iter	Nodes	Cost
0	105	581
1	215	530
2	471	507
3	1006	505
4	2547	502
done	5000	502

prune121.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
0.0b	(/ (* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))) x)
0.0b	(+ (sqrt (exp x)) (sqrt 1.0))
4.8b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-r`
8×	`frac-times` `add-cube-cbrt` `associate-/l/` `add-log-exp` `difference-of-squares`
7×	`flip3--` `flip3-+` `flip--` `flip-+`
6×	`pow1`
5×	`associate-l`
4×	`associate-r/` `associate-l/` `distribute-lft-out` `distribute-lft-out--`
3×	`sub-neg` `times-frac` `associate-/r*`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `sum-log` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

129.0ms	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
68.0ms	(/ (* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))) x)
17.0ms	(+ (sqrt (exp x)) (sqrt 1.0))
16.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series365.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
160.0ms	(/ (* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))) x)
36.0ms	(+ (sqrt (exp x)) (sqrt 1.0))
47.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify1.0s

Counts

110 → 110

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	146	1873
1	390	1304
2	1674	1172
done	5000	1171

prune247.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes28.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.4b

bsearch24.0ms

Steps

Iters	Range		Point
5	-0.00021785999598854965	-9.497075983896804e-05	-0.00012192187032837518

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	22	21
done	22	21

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.0s	2197×	body	1280	valid
331.0ms	1692×	body	640	valid
226.0ms	5367×	body	80	valid
102.0ms	852×	body	320	valid
32.0ms	417×	body	160	valid