Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	44×	body	1280	valid
6.0ms	46×	body	640	valid
4.0ms	141×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.4s

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	274	10
7	759	10
8	2522	10
done	5000	10

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

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))))
3.4b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite62.0ms

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))))
46.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series138.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
38.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
83.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.5s

Counts

150 → 150

Iterations

Useful iterations: 3 (588.0ms)

Iter	Nodes	Cost
0	180	3092
1	396	2501
2	866	2219
3	2487	1983
done	5000	1983

prune251.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
3.4b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite376.0ms

Algorithm

rewrite-expression-head

Rules

1732×	`times-frac`
1496×	`*-un-lft-identity`
1020×	`add-sqr-sqrt`
997×	`sqrt-prod`
996×	`add-cube-cbrt`
585×	`prod-diff`
249×	`distribute-lft-out`
195×	`fma-neg`
84×	`sqrt-div` `associate-/r/`
43×	`flip3-+` `flip-+`
42×	`div-inv`
30×	`associate-/l*`
14×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`difference-of-squares`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 1108

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
24.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
230.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series210.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ 1.0 (exp (* -2.0 x)))
37.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
71.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
85.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify1.7s

Counts

1120 → 1120

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	705	44341
1	1599	34715
2	3563	27922
done	5000	26887

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
0.1b	(* 0.33333333333333337 (pow x 3))
11.5b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`associate-r`
8×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `unpow3` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 62

Calls

3 calls:

3.0ms	(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
7.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(- (* 1.0 x) (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3))))
42.0ms	(* 0.33333333333333337 (pow x 3))
105.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify2.6s

Counts

71 → 71

Iterations

Useful iterations: 3 (995.0ms)

Iter	Nodes	Cost
0	112	1058
1	249	875
2	765	818
3	4077	781
done	5001	781

prune183.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes134.0ms

Accuracy

98.5% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 29.2b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	76
1	39	54
done	39	54

end0.0ms

sample863.0ms

Algorithm

intervals

Results

350.0ms	1698×	body	1280	valid
168.0ms	1231×	body	640	valid
111.0ms	4170×	body	80	valid
60.0ms	605×	body	320	valid
17.0ms	296×	body	160	valid