Details

sample86.0ms

Algorithm

intervals

Results

25.0ms	91×	body	10240	exit
25.0ms	69×	body	1280	valid
14.0ms	55×	body	640	valid
5.0ms	31×	body	320	valid
4.0ms	90×	body	80	valid
1.0ms	11×	body	160	valid

simplify8.0ms

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: 40.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1))
3.6b	(- (exp x) 1)

rewrite55.0ms

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:

41.0ms	(/ (exp x) (- (exp x) 1))
10.0ms	(- (exp x) 1)

series47.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1))
21.0ms	(- (exp x) 1)

simplify1.9s

Counts

69 → 69

Iterations

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

prune211.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite58.0ms

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:

50.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
7.0ms	(* 1/12 x)

series47.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
26.0ms	(* 1/12 x)

simplify1.9s

Counts

39 → 39

Iterations

Iter	Nodes
done	5006
3	1777
2	480
1	156
0	60

prune106.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (exp x) (+ (exp x) 1)) (- (exp x) 1))
0.3b	(* (/ (/ (exp x) (+ (exp x) 1)) (- (exp x) 1)) (+ (exp x) 1))
0.3b	(/ (exp x) (+ (exp x) 1))
3.6b	(- (exp x) 1)

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

447×	`times-frac`
386×	`*-un-lft-identity`
333×	`add-sqr-sqrt`
172×	`add-cube-cbrt`
132×	`associate-l`
76×	`difference-of-squares`
50×	`distribute-lft-out`
38×	`difference-of-sqr-1` `distribute-lft-out--`
36×	`associate-/r/`
21×	`associate-/l*`
20×	`add-cbrt-cube`
18×	`flip3-+` `flip-+` `div-inv`
17×	`add-exp-log`
11×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
4×	`associate-r` `insert-posit16`
3×	`flip3--` `prod-exp` `cbrt-unprod` `flip--` `unswap-sqr`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*r/`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 382

Calls

4 calls:

55.0ms	(/ (/ (exp x) (+ (exp x) 1)) (- (exp x) 1))
160.0ms	(* (/ (/ (exp x) (+ (exp x) 1)) (- (exp x) 1)) (+ (exp x) 1))
30.0ms	(/ (exp x) (+ (exp x) 1))
16.0ms	(- (exp x) 1)

series227.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (/ (exp x) (+ (exp x) 1)) (- (exp x) 1))
46.0ms	(* (/ (/ (exp x) (+ (exp x) 1)) (- (exp x) 1)) (+ (exp x) 1))
37.0ms	(/ (exp x) (+ (exp x) 1))
17.0ms	(- (exp x) 1)

simplify1.6s

Counts

394 → 394

Iterations

Iter	Nodes
done	5000
1	1513
0	389

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (* (exp x) (* (exp x) (exp x))) -1) (+ (+ (exp x) 1) (* (exp x) (exp x))))
0.3b	(* (/ (/ (exp x) (+ (exp x) 1)) (/ (+ (* (exp x) (* (exp x) (exp x))) -1) (+ (+ (exp x) 1) (* (exp x) (exp x))))) (+ (exp x) 1))
0.3b	(/ (exp x) (+ (exp x) 1))
3.6b	(+ (* (exp x) (* (exp x) (exp x))) -1)

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

641×	`times-frac`
369×	`*-un-lft-identity`
287×	`add-sqr-sqrt`
275×	`associate-l`
269×	`add-cube-cbrt`
71×	`associate-/r/`
50×	`distribute-lft-out`
39×	`flip3-+` `flip-+`
36×	`div-inv`
26×	`add-cbrt-cube`
23×	`add-exp-log`
10×	`cbrt-undiv` `div-exp`
7×	`associate-/r*`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`associate-r` `insert-posit16`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*r/` `associate-/l/`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 389

Calls

4 calls:

308.0ms	(/ (+ (* (exp x) (* (exp x) (exp x))) -1) (+ (+ (exp x) 1) (* (exp x) (exp x))))
564.0ms	(* (/ (/ (exp x) (+ (exp x) 1)) (/ (+ (* (exp x) (* (exp x) (exp x))) -1) (+ (+ (exp x) 1) (* (exp x) (exp x))))) (+ (exp x) 1))
22.0ms	(/ (exp x) (+ (exp x) 1))
61.0ms	(+ (* (exp x) (* (exp x) (exp x))) -1)

series327.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (* (exp x) (* (exp x) (exp x))) -1) (+ (+ (exp x) 1) (* (exp x) (exp x))))
143.0ms	(* (/ (/ (exp x) (+ (exp x) 1)) (/ (+ (* (exp x) (* (exp x) (exp x))) -1) (+ (+ (exp x) 1) (* (exp x) (exp x))))) (+ (exp x) 1))
34.0ms	(/ (exp x) (+ (exp x) 1))
50.0ms	(+ (* (exp x) (* (exp x) (exp x))) -1)

simplify3.7s

Counts

401 → 401

Iterations

Iter	Nodes
done	5003
1	3125
0	618

prune2.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes126.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 21.2b

bsearch1.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	34
1	34
0	25

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	2428×	body	10240	exit
866.0ms	2245×	body	1280	valid
444.0ms	1667×	body	640	valid
163.0ms	828×	body	320	valid
129.0ms	2832×	body	80	valid
41.0ms	431×	body	160	valid