Details

sample120.0ms

Algorithm

intervals

Results

40.0ms	94×	body	10240	exit
38.0ms	72×	body	1280	valid
16.0ms	47×	body	640	valid
7.0ms	99×	body	80	valid
6.0ms	23×	body	320	valid
2.0ms	15×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	5

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.8b	(/ (exp x) (- (exp x) 1))
4.2b	(- (exp x) 1)

rewrite51.0ms

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:

36.0ms	(/ (exp x) (- (exp x) 1))
13.0ms	(- (exp x) 1)

series53.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (exp x) (- (exp x) 1))
22.0ms	(- (exp x) 1)

simplify1.1s

Counts

69 → 69

Iterations

Iter	Nodes
done	2018
4	2018
3	1632
2	502
1	203
0	101

prune174.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

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)

rewrite37.0ms

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` `insert-posit16`
2×	`+-commutative` `flip3-+` `flip-+` `distribute-lft-out`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

8.0ms	(+ (/ 1 x) 1/2)
23.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
5.0ms	(* 1/12 x)

series55.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ (/ 1 x) 1/2)
15.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
21.0ms	(* 1/12 x)

simplify996.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2004
3	2004
2	723
1	210
0	76

prune181.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 x) 1/2)
0.0b	(+ (posit16->real (real->posit16 (* 1/12 x))) (+ (/ 1 x) 1/2))
0.3b	(* 1/12 x)
59.5b	(posit16->real (real->posit16 (* 1/12 x)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

8.0ms	(+ (/ 1 x) 1/2)
44.0ms	(+ (posit16->real (real->posit16 (* 1/12 x))) (+ (/ 1 x) 1/2))
5.0ms	(* 1/12 x)
0.0ms	(posit16->real (real->posit16 (* 1/12 x)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (/ 1 x) 1/2)
26.0ms	(+ (posit16->real (real->posit16 (* 1/12 x))) (+ (/ 1 x) 1/2))
26.0ms	(* 1/12 x)
17.0ms	(posit16->real (real->posit16 (* 1/12 x)))

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	2000
3	2000
2	752
1	223
0	86

prune466.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))
0.5b	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.5b	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
0.5b	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

196.0ms	(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))
17.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
17.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
38.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))) (cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2))))
130.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
125.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))
106.0ms	(cbrt (+ (* 1/12 x) (+ (/ 1 x) 1/2)))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	2001
3	2001
2	1084
1	371
0	152

prune518.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.7b

regimes251.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 21.9b

bsearch53.0ms

Steps

Iters	Range		Point
8	-0.0009127344879205425	-1.3816842601692823e-07	-2.9436761867628915e-05

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	2317×	body	1280	valid
1.2s	2532×	body	10240	exit
462.0ms	1580×	body	640	valid
199.0ms	2916×	body	80	valid
190.0ms	794×	body	320	valid
56.0ms	394×	body	160	valid