Details

sample117.0ms

Algorithm

intervals

Results

37.0ms	76×	body	1280	valid
36.0ms	75×	body	10240	exit
15.0ms	50×	body	640	valid
6.0ms	91×	body	80	valid
5.0ms	26×	body	320	valid
2.0ms	13×	body	160	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize59.0ms

Local error

Found 2 expressions with local error:

1.2b	(/ (exp x) (- (exp x) 1.0))
3.2b	(- (exp x) 1.0)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
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 → 53

Calls

2 calls:

69.0ms	(/ (exp x) (- (exp x) 1.0))
48.0ms	(- (exp x) 1.0)

series75.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (exp x) (- (exp x) 1.0))
21.0ms	(- (exp x) 1.0)

simplify3.4s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
3	1518
2	542
1	193
0	93

prune457.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize123.0ms

Local error

Found 4 expressions with local error:

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

rewrite396.0ms

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-+l+` `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:

57.0ms	(+ (* (* x x) (+ (* 1/6 x) 1/2)) x)
171.0ms	(/ (exp x) (+ (* (* x x) (+ (* 1/6 x) 1/2)) x))
149.0ms	(* (* x x) (+ (* 1/6 x) 1/2))
14.0ms	(* 1/6 x)

series260.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* (* x x) (+ (* 1/6 x) 1/2)) x)
71.0ms	(/ (exp x) (+ (* (* x x) (+ (* 1/6 x) 1/2)) x))
116.0ms	(* (* x x) (+ (* 1/6 x) 1/2))
27.0ms	(* 1/6 x)

simplify3.6s

Counts

99 → 99

Iterations

Iter	Nodes
done	5014
2	1489
1	425
0	162

prune995.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.1b

localize71.0ms

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)

rewrite198.0ms

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:

59.0ms	(+ (/ 1 x) 1/2)
121.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
14.0ms	(* 1/12 x)

series64.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ (/ 1 x) 1/2)
19.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
29.0ms	(* 1/12 x)

simplify7.7s

Counts

56 → 56

Iterations

Iter	Nodes
done	5001
3	3638
2	730
1	212
0	76

prune516.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize128.0ms

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)))

rewrite226.0ms

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:

56.0ms	(+ (/ 1 x) 1/2)
149.0ms	(+ (posit16->real (real->posit16 (* 1/12 x))) (+ (/ 1 x) 1/2))
15.0ms	(* 1/12 x)
1.0ms	(posit16->real (real->posit16 (* 1/12 x)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (/ 1 x) 1/2)
34.0ms	(+ (posit16->real (real->posit16 (* 1/12 x))) (+ (/ 1 x) 1/2))
26.0ms	(* 1/12 x)
19.0ms	(posit16->real (real->posit16 (* 1/12 x)))

simplify6.6s

Counts

71 → 71

Iterations

Iter	Nodes
done	5030
3	3328
2	710
1	224
0	86

prune750.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

regimes334.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	14
1	14
0	10

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	2564×	body	10240	exit
916.0ms	2148×	body	1280	valid
527.0ms	1647×	body	640	valid
235.0ms	2958×	body	80	valid
164.0ms	828×	body	320	valid
56.0ms	420×	body	160	valid