Details

sample63.0ms

Algorithm

intervals

Results

20.0ms	69×	body	1280	valid
15.0ms	65×	body	10240	exit
11.0ms	47×	body	640	valid
4.0ms	93×	body	80	valid
4.0ms	26×	body	320	valid
2.0ms	21×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1))
5.9b	(- (exp x) 1)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 63

Calls

2 calls:

37.0ms	(/ (exp x) (- (exp x) 1))
8.0ms	(- (exp x) 1)

series62.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (exp x) (- (exp x) 1))
25.0ms	(- (exp x) 1)

simplify2.0s

Counts

69 → 69

Iterations

Iter	Nodes
done	5010
3	1632
2	502
1	203
0	101

prune181.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l`
2×	`insert-posit16`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

23.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
5.0ms	(* 1/12 x)

series38.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
19.0ms	(* 1/12 x)

simplify1.6s

Counts

39 → 39

Iterations

Iter	Nodes
done	5006
3	1777
2	480
1	156
0	60

prune152.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

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))

rewrite30.0ms

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` `insert-posit16` `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 → 62

Calls

4 calls:

20.0ms	(* (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))

series1.3s

Counts

4 → 12

Calls

4 calls:

379.0ms	(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
346.0ms	(cbrt (* 1/12 x))
287.0ms	(cbrt (* 1/12 x))
241.0ms	(cbrt (* 1/12 x))

simplify2.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
4	2719
3	821
2	344
1	137
0	57

prune338.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* 1/12 x))
0.6b	(cbrt (* 1/12 x))
0.6b	(cbrt (* 1/12 x))
58.9b	(posit16->real (real->posit16 (* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`remove-posit16`

Counts

4 → 39

Calls

4 calls:

5.0ms	(cbrt (* 1/12 x))
4.0ms	(cbrt (* 1/12 x))
2.0ms	(cbrt (* 1/12 x))
0.0ms	(posit16->real (real->posit16 (* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

289.0ms	(cbrt (* 1/12 x))
312.0ms	(cbrt (* 1/12 x))
283.0ms	(cbrt (* 1/12 x))
339.0ms	(posit16->real (real->posit16 (* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))))

simplify2.6s

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
5	3984
4	1012
3	363
2	158
1	70
0	40

prune638.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

regimes160.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 21.6b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	28
1	28
0	21

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	2466×	body	10240	exit
1.0s	2237×	body	1280	valid
992.0ms	1593×	body	640	valid
182.0ms	2900×	body	80	valid
170.0ms	850×	body	320	valid
90.0ms	423×	body	160	valid