Details

sample32.0ms

Algorithm

intervals

Results

11.0ms	55×	body	1280	valid
7.0ms	47×	body	640	valid
3.0ms	126×	body	80	valid
2.0ms	20×	body	320	valid
0.0ms	8×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	15	10
2	22	10
3	31	10
4	55	10
5	113	10
6	260	10
7	727	10
8	2499	10
done	5001	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.6b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 141

Calls

3 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
40.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series130.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
40.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
74.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.3s

Counts

150 → 150

Iterations

Useful iterations: 3 (538.0ms)

Iter	Nodes	Cost
0	180	3092
1	378	2501
2	853	2219
3	2486	1983
done	5000	1983

prune263.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
8.1b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 43

Calls

2 calls:

6.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series137.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* 0.33333333333333337 (pow x 3))
102.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify1.5s

Counts

49 → 49

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	70	445
1	145	409
2	395	369
3	1851	369
done	5001	369

prune113.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(cbrt (+ 1.0 (exp (* -2.0 x))))
2.6b	(- (/ (/ 2.0 (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) 1.0)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

197×	`times-frac`
138×	`*-un-lft-identity`
117×	`prod-diff`
116×	`add-sqr-sqrt`
106×	`add-cube-cbrt`
62×	`cbrt-div`
61×	`cbrt-prod`
40×	`associate-/r/`
39×	`fma-neg`
31×	`flip3-+` `flip-+`
16×	`frac-times`
15×	`distribute-lft-out`
8×	`associate-r/` `associate-l/` `div-inv`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 223

Calls

4 calls:

2.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
2.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
2.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
105.0ms	(- (/ (/ 2.0 (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) 1.0)

series473.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
135.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
126.0ms	(cbrt (+ 1.0 (exp (* -2.0 x))))
78.0ms	(- (/ (/ 2.0 (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (+ 1.0 (exp (* -2.0 x)))) (cbrt (+ 1.0 (exp (* -2.0 x)))))) 1.0)

simplify726.0ms

Counts

235 → 235

Iterations

Useful iterations: done (716.0ms)

Iter	Nodes	Cost
0	322	8799
1	641	7474
2	1713	5766
done	5000	5571

prune501.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes144.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.2b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	88
1	38	58
done	38	58

end0.0ms

sample876.0ms

Algorithm

intervals

Results

349.0ms	1646×	body	1280	valid
187.0ms	1260×	body	640	valid
114.0ms	4136×	body	80	valid
57.0ms	620×	body	320	valid
20.0ms	338×	body	160	valid