Details

sample42.0ms

Algorithm

intervals

Results

12.0ms	87×	body	10240	exit
11.0ms	67×	body	1280	valid
5.0ms	48×	body	640	valid
2.0ms	103×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	8	7
done	8	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize4.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
4.1b	(- (exp x) 1.0)

rewrite15.0ms

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/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

8.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series45.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

57 → 57

Iterations

Useful iterations: 4 (596.0ms)

Iter	Nodes	Cost
0	91	640
1	181	614
2	422	579
3	927	577
4	2546	576
done	5001	576

prune124.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`sum-log`
3×	`associate-r` `associate-l`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

16.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
6.0ms	(+ (* 1/12 x) (/ 1 x))
3.0ms	(* 1/12 x)

series74.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1/2 (+ (* 1/12 x) (/ 1 x)))
44.0ms	(+ (* 1/12 x) (/ 1 x))
15.0ms	(* 1/12 x)

simplify1.0s

Counts

52 → 52

Iterations

Useful iterations: 3 (279.0ms)

Iter	Nodes	Cost
0	73	503
1	205	450
2	514	424
3	1540	422
done	5000	422

prune85.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
4.1b	(- 1 (/ 1.0 (exp x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
43×	`times-frac`
24×	`add-cube-cbrt`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`div-exp`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--` `div-inv`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 97

Calls

3 calls:

3.0ms	(/ 1.0 (exp x))
21.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
9.0ms	(- 1 (/ 1.0 (exp x)))

series112.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/ 1.0 (exp x))
58.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
38.0ms	(- 1 (/ 1.0 (exp x)))

simplify3.9s

Counts

106 → 106

Iterations

Useful iterations: 4 (2.8s)

Iter	Nodes	Cost
0	162	1303
1	310	1155
2	599	1099
3	1439	1094
4	4913	1092
done	5000	1092

prune151.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (- (* 0.16666666666666666 x) 0.5)) 1.0)
0.1b	(* x (- (* 0.16666666666666666 x) 0.5))
0.1b	(* x (+ (* x (- (* 0.16666666666666666 x) 0.5)) 1.0))
0.1b	(/ 1 (* x (+ (* x (- (* 0.16666666666666666 x) 0.5)) 1.0)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r/` `associate-r` `associate-l*` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
4×	`sub-neg` `associate-+l+` `div-exp`
3×	`flip3-+` `times-frac` `pow-prod-down` `cbrt-unprod` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `pow-flip` `1-exp` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`+-commutative` `flip3--` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `flip--` `div-inv` `inv-pow`

Counts

4 → 91

Calls

4 calls:

6.0ms	(+ (* x (- (* 0.16666666666666666 x) 0.5)) 1.0)
11.0ms	(* x (- (* 0.16666666666666666 x) 0.5))
21.0ms	(* x (+ (* x (- (* 0.16666666666666666 x) 0.5)) 1.0))
20.0ms	(/ 1 (* x (+ (* x (- (* 0.16666666666666666 x) 0.5)) 1.0)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (* x (- (* 0.16666666666666666 x) 0.5)) 1.0)
66.0ms	(* x (- (* 0.16666666666666666 x) 0.5))
45.0ms	(* x (+ (* x (- (* 0.16666666666666666 x) 0.5)) 1.0))
61.0ms	(/ 1 (* x (+ (* x (- (* 0.16666666666666666 x) 0.5)) 1.0)))

simplify2.0s

Counts

103 → 103

Iterations

Useful iterations: 3 (819.0ms)

Iter	Nodes	Cost
0	159	1437
1	390	1370
2	1064	1188
3	4446	1182
done	5000	1182

prune161.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes61.0ms

Accuracy

92.6% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 7.5b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	21	22
done	21	22

end0.0ms

sample1.1s

Algorithm

intervals

Results

387.0ms	2224×	body	1280	valid
282.0ms	2499×	body	10240	exit
180.0ms	1625×	body	640	valid
61.0ms	844×	body	320	valid
56.0ms	2881×	body	80	valid
20.0ms	427×	body	160	valid