Details

sample49.0ms

Algorithm

intervals

Results

17.0ms	83×	body	1280	valid
12.0ms	79×	body	10240	exit
7.0ms	49×	body	640	valid
2.0ms	88×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ (exp x) (- (exp x) 1))
2.5b	(- (exp x) 1)

rewrite33.0ms

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:

24.0ms	(/ (exp x) (- (exp x) 1))
8.0ms	(- (exp x) 1)

series42.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (exp x) (- (exp x) 1))
15.0ms	(- (exp x) 1)

simplify1.7s

Counts

69 → 69

Iterations

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

prune257.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.4b	(* 1/12 x)

rewrite28.0ms

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)

series36.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(+ (* 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

prune151.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize26.0ms

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)

rewrite21.0ms

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` `insert-posit16` `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 → 77

Calls

4 calls:

15.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.0s

Counts

4 → 12

Calls

4 calls:

282.0ms	(* (cbrt x) (cbrt x))
264.0ms	(cbrt x)
236.0ms	(cbrt x)
261.0ms	(cbrt x)

simplify3.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5002
4	3832
3	1045
2	380
1	138
0	63

prune446.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
59.2b	(posit16->real (real->posit16 (* (cbrt x) (cbrt x))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

4 calls:

1.0ms	(cbrt x)
5.0ms	(cbrt x)
1.0ms	(cbrt x)
0.0ms	(posit16->real (real->posit16 (* (cbrt x) (cbrt x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

291.0ms	(cbrt x)
312.0ms	(cbrt x)
242.0ms	(cbrt x)
294.0ms	(posit16->real (real->posit16 (* (cbrt x) (cbrt x))))

simplify1.4s

Counts

57 → 57

Iterations

Iter	Nodes
done	5000
4	1263
3	457
2	196
1	81
0	44

prune595.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

regimes57.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 21.7b

bsearch47.0ms

Steps

Iters	Range		Point
9	-34.11472770615283	-3.67231414207575e-08	-4.450925509850113e-05

simplify6.0ms

Iterations

Iter	Nodes
done	38
1	38
0	28

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	2544×	body	10240	exit
836.0ms	2224×	body	1280	valid
424.0ms	1632×	body	640	valid
166.0ms	2907×	body	80	valid
128.0ms	821×	body	320	valid
42.0ms	420×	body	160	valid