Details

sample96.0ms

Algorithm

intervals

Results

38.0ms	56×	body	1280	valid
19.0ms	40×	body	640	valid
12.0ms	119×	body	80	valid
11.0ms	33×	body	320	valid
2.0ms	8×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
8	2490
7	682
6	240
5	101
4	51
3	30
2	22
1	18
0	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
3.1b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
63×	`times-frac` `add-cube-cbrt`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-exp-log`
7×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`add-cbrt-cube` `div-inv`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `fma-def` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`expm1-def` `difference-of-sqr-1` `div-exp`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 150

Calls

3 calls:

19.0ms	(+ 1 (exp (* -2 x)))
45.0ms	(/ 2 (+ 1 (exp (* -2 x))))
268.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series135.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ 1 (exp (* -2 x)))
42.0ms	(/ 2 (+ 1 (exp (* -2 x))))
74.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify3.0s

Counts

159 → 159

Iterations

Iter	Nodes
done	5000
3	2671
2	930
1	426
0	183

prune536.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma -1/3 (* x (* x x)) x)
0.1b	(* x (* x x))
18.1b	(fma (pow x 5) 2/15 (fma -1/3 (* x (* x x)) x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`associate-r`
17×	`pow1`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
7×	`unswap-sqr`
6×	`associate-l`
5×	`pow-prod-up`
4×	`swap-sqr` `*-commutative`
3×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cube-unmult` `fma-udef`
1×	`pow2` `pow-plus` `pow-sqr`

Counts

3 → 68

Calls

3 calls:

1.0ms	(fma -1/3 (* x (* x x)) x)
55.0ms	(* x (* x x))
1.0ms	(fma (pow x 5) 2/15 (fma -1/3 (* x (* x x)) x))

series268.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(fma -1/3 (* x (* x x)) x)
43.0ms	(* x (* x x))
83.0ms	(fma (pow x 5) 2/15 (fma -1/3 (* x (* x x)) x))

simplify1.1s

Counts

77 → 77

Iterations

Iter	Nodes
done	5009
2	732
1	202
0	92

prune317.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2 (+ 1 (exp (* x -2))))
0.0b	(+ 1 (exp (* x -2)))
3.1b	(- (/ 2 (+ 1 (exp (* x -2)))) 1)

rewrite396.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
63×	`times-frac` `add-cube-cbrt`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-exp-log`
7×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`add-cbrt-cube` `div-inv`
4×	`associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `pow1` `fma-def` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`expm1-def` `difference-of-sqr-1` `div-exp`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 150

Calls

3 calls:

38.0ms	(/ 2 (+ 1 (exp (* x -2))))
25.0ms	(+ 1 (exp (* x -2)))
321.0ms	(- (/ 2 (+ 1 (exp (* x -2)))) 1)

series133.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(/ 2 (+ 1 (exp (* x -2))))
20.0ms	(+ 1 (exp (* x -2)))
82.0ms	(- (/ 2 (+ 1 (exp (* x -2)))) 1)

simplify3.0s

Counts

159 → 159

Iterations

Iter	Nodes
done	5000
3	2770
2	1079
1	432
0	185

prune460.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes92.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.2b

bsearch183.0ms

Steps

Iters	Range		Point
9	6.802190297852232e-07	2.2608459371195293	0.0076963482510729354
10	-271299687514.82303	-4.981612762678325e-05	-0.007956784398241263

simplify10.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	1776×	body	1280	valid
565.0ms	1256×	body	640	valid
346.0ms	3972×	body	80	valid
195.0ms	650×	body	320	valid
56.0ms	346×	body	160	valid