Details

sample47.0ms

Algorithm

intervals

Results

14.0ms	37×	body	1280	valid
10.0ms	38×	body	640	valid
9.0ms	152×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	6×	body	160	valid

simplify13.9s

Counts

1 → 1

Iterations

Iter	Nodes
9	9892
8	1985
7	571
6	236
5	102
4	50
3	29
2	22
1	18
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2 (+ 1 (exp (* -2 x))))
0.0b	(+ 1 (exp (* -2 x)))
1.9b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
15×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `difference-of-squares`
3×	`pow1` `insert-posit16` `associate-/l*`
2×	`flip3-+` `difference-of-sqr-1` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `distribute-lft-out--`

Counts

3 → 67

Calls

3 calls:

16.0ms	(/ 2 (+ 1 (exp (* -2 x))))
5.0ms	(+ 1 (exp (* -2 x)))
69.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series111.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ 2 (+ 1 (exp (* -2 x))))
17.0ms	(+ 1 (exp (* -2 x)))
74.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify2.9s

Counts

76 → 76

Iterations

Iter	Nodes
4	3581
3	1360
2	598
1	266
0	120

prune753.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))
0.0b	(/ (- (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x))))) 1) (+ 1 (* (+ (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x)))))))
0.0b	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
1.8b	(- (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x))))) 1)

rewrite569.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
34×	`flip3-+` `flip-+`
32×	`frac-times`
28×	`associate-/r/`
24×	`times-frac`
22×	`add-cube-cbrt`
17×	`add-cbrt-cube` `add-exp-log`
16×	`associate-*l/`
11×	`pow1`
10×	`associate-r/` `associate-/l` `difference-of-squares`
6×	`swap-sqr` `distribute-lft-out` `add-log-exp`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`cbrt-undiv` `associate-/r` `div-exp` `associate-r` `associate-l*` `prod-exp` `cbrt-unprod` `insert-posit16`
2×	`clear-num` `frac-2neg` `flip3--` `div-inv` `flip--` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 157

Calls

4 calls:

58.0ms	(* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))
322.0ms	(/ (- (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x))))) 1) (+ 1 (* (+ (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x)))))))
62.0ms	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
123.0ms	(- (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x))))) 1)

series517.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))
319.0ms	(/ (- (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x))))) 1) (+ 1 (* (+ (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x)))))))
49.0ms	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
116.0ms	(- (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x))))) 1)

simplify1.3s

Counts

169 → 169

Iterations

Iter	Nodes
2	3001
1	878
0	279

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
0.0b	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
0.0b	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
1.8b	(- (* (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x))))) (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))) (* 1 1))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

84×	`frac-times`
81×	`flip3-+` `flip-+`
78×	`associate-/r/`
42×	`associate-*l/`
31×	`add-cbrt-cube` `add-exp-log`
24×	`associate-*r/`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-undiv` `times-frac` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
6×	`add-log-exp`
4×	`pow1` `insert-posit16`
3×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 164

Calls

4 calls:

46.0ms	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
46.0ms	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
52.0ms	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
318.0ms	(- (* (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x))))) (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))) (* 1 1))

series259.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
42.0ms	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
57.0ms	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
118.0ms	(- (* (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x))))) (/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))) (* 1 1))

simplify3.3s

Counts

176 → 176

Iterations

Iter	Nodes
3	7128
2	1943
1	515
0	168

prune2.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize162.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
0.0b	(* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))))
0.0b	(* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))))
1.7b	(- (* (/ 512 (* (* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))))) (/ 512 (* (* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))))))) 1)

rewrite11.6s

Algorithm

rewrite-expression-head

Rules

4404×	`frac-times`
2943×	`flip3-+` `flip-+`
1572×	`associate-*r/`
930×	`associate-*l/`
524×	`pow1`
232×	`pow-prod-up`
146×	`pow-prod-down`
85×	`add-cbrt-cube` `add-exp-log`
60×	`pow-sqr`
57×	`prod-exp` `cbrt-unprod`
42×	`pow-plus`
30×	`pow2`
28×	`cube-unmult`
26×	`associate-/r/`
24×	`distribute-rgt-in` `distribute-lft-in`
7×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`add-cube-cbrt` `add-log-exp`
4×	`insert-posit16`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `difference-of-squares`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `flip3--` `diff-log` `difference-of-sqr-1` `div-inv` `flip--`

Counts

4 → 1738

Calls

4 calls:

68.0ms	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
506.0ms	(* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))))
381.0ms	(* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))))
10.5s	(- (* (/ 512 (* (* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))))) (/ 512 (* (* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))))))) 1)

series332.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ 8 (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
62.0ms	(* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))))
53.0ms	(* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))))
149.0ms	(- (* (/ 512 (* (* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))))) (/ 512 (* (* (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))))) (* (+ 1 (exp (* -2 x))) (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))))))) 1)

simplify5.5s

Counts

1750 → 1750

Iterations

Iter	Nodes
1	4493
0	1224

prune58.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes521.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.1b

bsearch3.0ms

simplify23.0ms

Iterations

Iter	Nodes
3	72
2	72
1	71
0	54

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	1763×	body	1280	valid
578.0ms	1192×	body	640	valid
375.0ms	4116×	body	80	valid
204.0ms	621×	body	320	valid
54.0ms	308×	body	160	valid