Details

sample91.0ms

Algorithm

intervals

Results

41.0ms	72×	body	1280	valid
16.0ms	47×	body	640	valid
12.0ms	169×	body	80	valid
9.0ms	36×	body	320	valid
2.0ms	13×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	18
3	18
2	16
1	13
0	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
4.7b	(- (exp x) 1)

rewrite39.0ms

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-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 64

Calls

2 calls:

21.0ms	(/ (- (exp x) 1) x)
17.0ms	(- (exp x) 1)

series76.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1) x)
31.0ms	(- (exp x) 1)

simplify1.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	5004
3	1887
2	592
1	239
0	108

prune208.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (* x (+ 1/2 (* 1/6 x))))
0.0b	(+ 1/2 (* 1/6 x))
0.1b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

5.0ms	(+ 1 (* x (+ 1/2 (* 1/6 x))))
4.0ms	(+ 1/2 (* 1/6 x))
11.0ms	(* x (+ 1/2 (* 1/6 x)))
8.0ms	(* 1/6 x)

series201.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ 1 (* x (+ 1/2 (* 1/6 x))))
60.0ms	(+ 1/2 (* 1/6 x))
86.0ms	(* x (+ 1/2 (* 1/6 x)))
16.0ms	(* 1/6 x)

simplify1.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	909
1	298
0	105

prune292.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/6 x)
0.4b	(* 1/6 x)
0.4b	(* 1/6 x)
12.5b	(/ (- 1 (* (* x (+ 1/2 (* 1/6 x))) (* x (+ 1/2 (* 1/6 x))))) (- 1 (* x (+ 1/2 (* 1/6 x)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`add-cube-cbrt`
15×	`times-frac`
12×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-r` `associate-l`
8×	`difference-of-squares`
5×	`associate-/l*`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

4 → 98

Calls

4 calls:

10.0ms	(* 1/6 x)
7.0ms	(* 1/6 x)
5.0ms	(* 1/6 x)
19.0ms	(/ (- 1 (* (* x (+ 1/2 (* 1/6 x))) (* x (+ 1/2 (* 1/6 x))))) (- 1 (* x (+ 1/2 (* 1/6 x)))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* 1/6 x)
23.0ms	(* 1/6 x)
17.0ms	(* 1/6 x)
76.0ms	(/ (- 1 (* (* x (+ 1/2 (* 1/6 x))) (* x (+ 1/2 (* 1/6 x))))) (- 1 (* x (+ 1/2 (* 1/6 x)))))

simplify3.1s

Counts

110 → 110

Iterations

Iter	Nodes
done	5002
3	4862
2	876
1	303
0	123

prune472.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/6 x)
0.4b	(* 1/6 x)
12.5b	(/ (- 1 (* (* x (+ 1/2 (posit16->real (real->posit16 (* 1/6 x))))) (* x (+ 1/2 (* 1/6 x))))) (- 1 (* x (+ 1/2 (* 1/6 x)))))
59.9b	(posit16->real (real->posit16 (* 1/6 x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube` `add-exp-log`
9×	`times-frac`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv` `remove-posit16`

Counts

4 → 80

Calls

4 calls:

9.0ms	(* 1/6 x)
6.0ms	(* 1/6 x)
24.0ms	(/ (- 1 (* (* x (+ 1/2 (posit16->real (real->posit16 (* 1/6 x))))) (* x (+ 1/2 (* 1/6 x))))) (- 1 (* x (+ 1/2 (* 1/6 x)))))
1.0ms	(posit16->real (real->posit16 (* 1/6 x)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 1/6 x)
28.0ms	(* 1/6 x)
88.0ms	(/ (- 1 (* (* x (+ 1/2 (posit16->real (real->posit16 (* 1/6 x))))) (* x (+ 1/2 (* 1/6 x))))) (- 1 (* x (+ 1/2 (* 1/6 x)))))
18.0ms	(posit16->real (real->posit16 (* 1/6 x)))

simplify2.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	1020
1	291
0	118

prune734.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes47.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.2b

bsearch25.0ms

Steps

Iters	Range		Point
6	-0.0005350557287305616	-5.532094628653386e-05	-9.8136436745457e-05

simplify7.0ms

Iterations

Iter	Nodes
done	33
1	33
0	22

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	2277×	body	1280	valid
506.0ms	1638×	body	640	valid
331.0ms	5311×	body	80	valid
169.0ms	900×	body	320	valid
58.0ms	466×	body	160	valid