Details

sample51.0ms

Algorithm

intervals

Results

13.0ms	64×	body	1280	valid
10.0ms	76×	body	10240	exit
7.0ms	16×	body	160	valid
6.0ms	49×	body	640	valid
3.0ms	98×	body	80	valid
2.0ms	29×	body	320	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: 39.7b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

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)

series54.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (exp x) (- (exp x) 1.0))
16.0ms	(- (exp x) 1.0)

simplify1.5s

Counts

57 → 57

Iterations

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

prune246.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (/ 1 x) 1/2)
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.3b	(* 1/12 x)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`sum-log`
3×	`associate-r` `associate-l`
2×	`+-commutative` `flip3-+` `flip-+` `distribute-lft-out`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

12.0ms	(+ (/ 1 x) 1/2)
40.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
7.0ms	(* 1/12 x)

series48.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(+ (/ 1 x) 1/2)
16.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
18.0ms	(* 1/12 x)

simplify903.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
2	774
1	209
0	73

prune251.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

9.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.2s

Counts

4 → 12

Calls

4 calls:

334.0ms	(* (cbrt x) (cbrt x))
261.0ms	(cbrt x)
309.0ms	(cbrt x)
260.0ms	(cbrt x)

simplify1.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	727
1	138
0	61

prune440.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize36.0ms

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))

rewrite36.0ms

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:

26.0ms	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
3.0ms	(cbrt (* 1/12 x))
3.0ms	(cbrt (* 1/12 x))
3.0ms	(cbrt (* 1/12 x))

series1.4s

Counts

4 → 12

Calls

4 calls:

395.0ms	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
362.0ms	(cbrt (* 1/12 x))
328.0ms	(cbrt (* 1/12 x))
299.0ms	(cbrt (* 1/12 x))

simplify956.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	575
1	137
0	55

prune344.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

regimes111.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 21.6b

bsearch1.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	40
1	40
0	29

end0.0ms

sample2.7s

Algorithm

intervals

Results

751.0ms	2544×	body	10240	exit
683.0ms	2289×	body	1280	valid
435.0ms	792×	body	320	valid
306.0ms	1611×	body	640	valid
148.0ms	2894×	body	80	valid
82.0ms	417×	body	160	valid