Details

sample61.0ms

Algorithm

intervals

Results

18.0ms	68×	body	1280	valid
16.0ms	94×	body	10240	exit
9.0ms	54×	body	640	valid
4.0ms	31×	body	320	valid
3.0ms	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)

rewrite36.0ms

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:

14.0ms	(/ (exp x) (- (exp x) 1.0))
8.0ms	(- (exp x) 1.0)

series46.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ (exp x) (- (exp x) 1.0))
17.0ms	(- (exp x) 1.0)

simplify1.2s

Counts

57 → 57

Iterations

Iter	Nodes
done	5002
3	1479
2	540
1	191
0	91

prune195.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite67.0ms

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:

35.0ms	(/ (exp x) (+ (* (* x x) (+ 1/2 (* 1/6 x))) x))
25.0ms	(* (* x x) (+ 1/2 (* 1/6 x)))
6.0ms	(* 1/6 x)

series154.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (exp x) (+ (* (* x x) (+ 1/2 (* 1/6 x))) x))
80.0ms	(* (* x x) (+ 1/2 (* 1/6 x)))
15.0ms	(* 1/6 x)

simplify1.4s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
2	1458
1	404
0	149

prune379.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 1 expressions with local error:

0.3b	(* 1/12 x)

rewrite12.0ms

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:

11.0ms

(* 1/12 x)

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

(* 1/12 x)

simplify1.8s

Counts

21 → 21

Iterations

Iter	Nodes
done	5000
6	1597
5	756
4	504
3	266
2	120
1	63
0	30

prune112.0ms

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))

rewrite32.0ms

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:

15.0ms	(* (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:

308.0ms	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
302.0ms	(cbrt (* 1/12 x))
336.0ms	(cbrt (* 1/12 x))
334.0ms	(cbrt (* 1/12 x))

simplify2.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5003
4	2640
3	771
2	322
1	134
0	55

prune328.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes37.0ms

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

1.1s	2597×	body	10240	exit
765.0ms	2334×	body	1280	valid
371.0ms	1560×	body	640	valid
104.0ms	868×	body	320	valid
94.0ms	2820×	body	80	valid
39.0ms	419×	body	160	valid