Details

sample49.0ms

Algorithm

intervals

Results

13.0ms	68×	body	1280	valid
12.0ms	94×	body	10240	exit
7.0ms	54×	body	640	valid
3.0ms	31×	body	320	valid
2.0ms	92×	body	80	valid
1.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
3.9b	(- (exp x) 1.0)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 51

Calls

2 calls:

19.0ms	(/ (exp x) (- (exp x) 1.0))
8.0ms	(- (exp x) 1.0)

series49.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ (exp x) (- (exp x) 1.0))
17.0ms	(- (exp x) 1.0)

simplify1.5s

Counts

57 → 57

Iterations

Iter	Nodes
done	5000
3	2908
2	645
1	191
0	91

prune268.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (+ (* (* x x) (+ (* x 1/6) 1/2)) x))
0.1b	(* (* x x) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

66.0ms	(/ (exp x) (+ (* (* x x) (+ (* x 1/6) 1/2)) x))
35.0ms	(* (* x x) (+ (* x 1/6) 1/2))
5.0ms	(* x 1/6)

series205.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (exp x) (+ (* (* x x) (+ (* x 1/6) 1/2)) x))
121.0ms	(* (* x x) (+ (* x 1/6) 1/2))
16.0ms	(* x 1/6)

simplify3.7s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
2	3109
1	431
0	150

prune376.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 1 expressions with local error:

0.3b	(* 1/12 x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt`
3×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp` `unswap-sqr`

Counts

1 → 18

Calls

1 calls:

5.0ms

(* 1/12 x)

series22.0ms

Counts

1 → 3

Calls

1 calls:

22.0ms

(* 1/12 x)

simplify2.0s

Counts

21 → 21

Iterations

Iter	Nodes
done	5001
5	2346
4	1251
3	484
2	157
1	65
0	30

prune116.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
0.6b	(cbrt (* 1/12 x))
0.6b	(cbrt (* 1/12 x))
0.6b	(cbrt (* 1/12 x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

22.0ms	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
5.0ms	(cbrt (* 1/12 x))
5.0ms	(cbrt (* 1/12 x))
5.0ms	(cbrt (* 1/12 x))

series1.3s

Counts

4 → 12

Calls

4 calls:

378.0ms	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
313.0ms	(cbrt (* 1/12 x))
277.0ms	(cbrt (* 1/12 x))
357.0ms	(cbrt (* 1/12 x))

simplify871.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	575
1	137
0	55

prune296.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes46.0ms

Accuracy

0% (0.2b remaining)

Error of 0.9b against oracle of 0.7b and baseline of 0.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	10

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.2s	2334×	body	1280	valid
635.0ms	2597×	body	10240	exit
333.0ms	1560×	body	640	valid
180.0ms	2820×	body	80	valid
107.0ms	868×	body	320	valid
70.0ms	419×	body	160	valid