Details

sample89.0ms

Algorithm

intervals

Results

60.0ms	184×	body	1280	valid
8.0ms	272×	body	80	valid
6.0ms	34×	body	640	valid
3.0ms	30×	body	320	valid
0.0ms	5×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
10	2899
9	809
8	249
7	88
6	71
5	62
4	56
3	40
2	26
1	14
0	7

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.5b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`neg-sub0` `exp-neg` `pow1` `associate-+l+` `sum-log` `sub-neg` `add-cbrt-cube` `exp-diff` `diff-log` `add-exp-log` `add-cube-cbrt` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

11.0ms	(- (exp x) 2.0)
48.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- (exp x) 2.0)
103.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify1.1s

Counts

41 → 41

Iterations

Iter	Nodes
done	5001
2	825
1	215
0	93

prune175.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* 1/12 (* (* x x) (* x x)))
0.1b	(* (* (* x x) x) 1/360)
0.1b	(* (* x x) (* x x))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

161×	`pow1`
48×	`add-cbrt-cube` `add-exp-log`
45×	`pow-prod-down`
42×	`pow-prod-up`
30×	`prod-exp` `cbrt-unprod`
24×	`pow-plus` `pow-sqr`
15×	`pow2`
9×	`add-sqr-sqrt`
8×	`associate-r`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`*-commutative` `add-log-exp`
3×	`unswap-sqr`
1×	`swap-sqr` `pow3`

Counts

4 → 140

Calls

4 calls:

14.0ms	(* (* x x) x)
89.0ms	(* 1/12 (* (* x x) (* x x)))
52.0ms	(* (* (* x x) x) 1/360)
33.0ms	(* (* x x) (* x x))

series222.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* x x) x)
63.0ms	(* 1/12 (* (* x x) (* x x)))
73.0ms	(* (* (* x x) x) 1/360)
34.0ms	(* (* x x) (* x x))

simplify3.9s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	2933
1	360
0	118

prune327.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp x) 2.0)
0.0b	(* (- (exp x) 2.0) (exp x))
0.0b	(* (+ 2.0 (exp x)) (+ 1 (* (- (exp x) 2.0) (exp x))))
3.7b	(+ 1 (* (- (exp x) 2.0) (exp x)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
9×	`associate-l`
8×	`pow1` `add-cbrt-cube` `add-cube-cbrt` `add-log-exp`
7×	`flip3-+` `add-exp-log` `flip-+`
6×	`associate-r`
4×	`frac-times` `associate-*l/`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `diff-log` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

8.0ms	(- (exp x) 2.0)
47.0ms	(* (- (exp x) 2.0) (exp x))
34.0ms	(* (+ 2.0 (exp x)) (+ 1 (* (- (exp x) 2.0) (exp x))))
13.0ms	(+ 1 (* (- (exp x) 2.0) (exp x)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (exp x) 2.0)
61.0ms	(* (- (exp x) 2.0) (exp x))
140.0ms	(* (+ 2.0 (exp x)) (+ 1 (* (- (exp x) 2.0) (exp x))))
93.0ms	(+ 1 (* (- (exp x) 2.0) (exp x)))

simplify3.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	3534
1	444
0	146

prune443.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize141.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.0b	(* (exp x) (exp x))
0.0b	(* (exp x) (exp x))
4.4b	(+ (* (* (- (exp x) 2.0) (* (- (exp x) 2.0) (- (exp x) 2.0))) (* (* (* (exp x) (exp x)) (exp x)) (+ (* (* (exp x) (exp x)) (exp x)) (* 2.0 (* 2.0 2.0))))) (+ (* (* (exp x) (exp x)) (exp x)) (* 2.0 (* 2.0 2.0))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

272×	`frac-times`
196×	`associate-*r/`
162×	`flip3--` `flip--`
160×	`frac-add`
135×	`flip3-+` `flip-+`
100×	`associate-*l/`
54×	`exp-prod`
40×	`add-sqr-sqrt`
34×	`*-un-lft-identity` `add-cube-cbrt`
25×	`pow1`
12×	`pow-prod-down` `pow-sqr` `pow-prod-up`
10×	`add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `add-exp-log`
3×	`pow2` `sum-log` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r+`

Counts

4 → 279

Calls

4 calls:

29.0ms	(* (exp x) (exp x))
24.0ms	(* (exp x) (exp x))
13.0ms	(* (exp x) (exp x))
1.3s	(+ (* (* (- (exp x) 2.0) (* (- (exp x) 2.0) (- (exp x) 2.0))) (* (* (* (exp x) (exp x)) (exp x)) (+ (* (* (exp x) (exp x)) (exp x)) (* 2.0 (* 2.0 2.0))))) (+ (* (* (exp x) (exp x)) (exp x)) (* 2.0 (* 2.0 2.0))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (exp x) (exp x))
23.0ms	(* (exp x) (exp x))
25.0ms	(* (exp x) (exp x))
543.0ms	(+ (* (* (- (exp x) 2.0) (* (- (exp x) 2.0) (- (exp x) 2.0))) (* (* (* (exp x) (exp x)) (exp x)) (+ (* (* (exp x) (exp x)) (exp x)) (* 2.0 (* 2.0 2.0))))) (+ (* (* (exp x) (exp x)) (exp x)) (* 2.0 (* 2.0 2.0))))

simplify3.3s

Counts

291 → 291

Iterations

Iter	Nodes
done	5001
1	3483
0	770

prune2.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	11

end0.0ms

sample5.0s

Algorithm

intervals

Results

3.5s	5680×	body	1280	valid
560.0ms	7954×	body	80	valid
441.0ms	1235×	body	640	valid
109.0ms	616×	body	320	valid
39.0ms	313×	body	160	valid