Details

sample109.0ms

Algorithm

intervals

Results

44.0ms	76×	body	1280	valid
26.0ms	75×	body	10240	exit
15.0ms	50×	body	640	valid
5.0ms	91×	body	80	valid
5.0ms	26×	body	320	valid
2.0ms	13×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize15.0ms

Local error

Found 2 expressions with local error:

1.2b	(/ (exp x) (- (exp x) 1))
3.2b	(- (exp x) 1)

rewrite45.0ms

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:

27.0ms	(/ (exp x) (- (exp x) 1))
16.0ms	(- (exp x) 1)

series53.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (exp x) (- (exp x) 1))
19.0ms	(- (exp x) 1)

simplify928.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
2	905
1	215
0	101

prune271.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`add-exp-log`
11×	`pow1`
9×	`times-frac`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-r/` `associate-/r/` `-commutative` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

9.0ms	(+ x (* (* x x) (+ 1/2 (* x 1/6))))
9.0ms	(/ (exp x) (+ x (* (* x x) (+ 1/2 (* x 1/6)))))
22.0ms	(* (* x x) (+ 1/2 (* x 1/6)))
5.0ms	(* x 1/6)

series198.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ x (* (* x x) (+ 1/2 (* x 1/6))))
62.0ms	(/ (exp x) (+ x (* (* x x) (+ 1/2 (* x 1/6)))))
81.0ms	(* (* x x) (+ 1/2 (* x 1/6)))
21.0ms	(* x 1/6)

simplify3.7s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	3277
1	462
0	163

prune398.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.1b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

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:

17.0ms	(+ (/ 1 x) 1/2)
30.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
5.0ms	(* 1/12 x)

series58.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+ (/ 1 x) 1/2)
16.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
22.0ms	(* 1/12 x)

simplify944.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
2	777
1	212
0	76

prune187.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize60.0ms

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))
0.4b	(* 1/12 x)
59.8b	(posit16->real (real->posit16 (* 1/12 x)))

rewrite38.0ms

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:

9.0ms	(+ (/ 1 x) 1/2)
22.0ms	(+ (posit16->real (real->posit16 (* 1/12 x))) (+ (/ 1 x) 1/2))
6.0ms	(* 1/12 x)
1.0ms	(posit16->real (real->posit16 (* 1/12 x)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (/ 1 x) 1/2)
19.0ms	(+ (posit16->real (real->posit16 (* 1/12 x))) (+ (/ 1 x) 1/2))
17.0ms	(* 1/12 x)
17.0ms	(posit16->real (real->posit16 (* 1/12 x)))

simplify988.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	810
1	228
0	86

prune573.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

regimes144.0ms

Accuracy

0% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 1.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	10

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	2564×	body	10240	exit
1.0s	2148×	body	1280	valid
570.0ms	1647×	body	640	valid
173.0ms	2958×	body	80	valid
160.0ms	828×	body	320	valid
53.0ms	420×	body	160	valid