Details

sample32.0ms

Algorithm

intervals

Results

14.0ms	77×	body	1280	valid
6.0ms	57×	body	640	valid
3.0ms	157×	body	80	valid
2.0ms	26×	body	320	valid
0.0ms	9×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 41.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
2.7b	(- (exp x) 1.0)

rewrite17.0ms

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:

11.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series58.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify1.2s

Counts

58 → 58

Iterations

Useful iterations: 3 (291.0ms)

Iter	Nodes	Cost
0	99	596
1	221	572
2	545	542
3	2066	537
done	5000	537

prune116.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1/2 (* x 1/6)))
0.3b	(* x 1/6)

rewrite11.0ms

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:

7.0ms	(* x (+ 1/2 (* x 1/6)))
3.0ms	(* x 1/6)

series71.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(* x (+ 1/2 (* x 1/6)))
13.0ms	(* x 1/6)

simplify1.3s

Counts

46 → 46

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	70	356
1	181	328
2	619	298
3	2583	298
done	5000	298

prune78.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (pow x 2) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)
4.2b	(/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log`
11×	`associate-l`
9×	`times-frac` `add-cbrt-cube`
6×	`associate-r`
5×	`pow1` `unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`associate-/r` `associate-/l` `add-log-exp`
2×	`flip3-+` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `div-inv`

Counts

3 → 78

Calls

3 calls:

13.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)
9.0ms	(/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x)

series125.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(* (pow x 2) (+ (* x 1/6) 1/2))
13.0ms	(* x 1/6)
47.0ms	(/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x)

simplify718.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (212.0ms)

Iter	Nodes	Cost
0	142	1212
1	367	1139
2	1445	1036
done	5000	1036

prune180.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

4.2b	(/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x)
4.2b	(/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x)
8.7b	(sqrt (/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x))
8.7b	(sqrt (/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
26×	`sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l`
4×	`rem-sqrt-square` `div-inv` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `clear-num` `flip-+`

Counts

4 → 108

Calls

4 calls:

11.0ms	(/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x)
9.0ms	(/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x)
5.0ms	(sqrt (/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x))
4.0ms	(sqrt (/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x))

series285.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x)
47.0ms	(/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x)
97.0ms	(sqrt (/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x))
97.0ms	(sqrt (/ (+ x (* (pow x 2) (+ (* x 1/6) 1/2))) x))

simplify2.2s

Counts

120 → 120

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	117	2622
1	247	2478
2	802	2288
3	4197	2260
done	5001	2258

prune353.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

regimes26.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch44.0ms

Steps

Iters	Range		Point
10	-64880754058.88788	-5.5985807885592334e-05	-0.00014985840866440616

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	43
1	43	43
done	43	43

end0.0ms

sample925.0ms

Algorithm

intervals

Results

408.0ms	2343×	body	1280	valid
184.0ms	1637×	body	640	valid
106.0ms	5409×	body	80	valid
58.0ms	811×	body	320	valid
18.0ms	401×	body	160	valid