Details

sample78.0ms

Algorithm

intervals

Results

34.0ms	61×	body	1280	valid
14.0ms	42×	body	640	valid
9.0ms	121×	body	80	valid
5.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3471
6	531
5	151
4	61
3	33
2	24
1	18
0	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
2.7b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite120.0ms

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:

13.0ms	(+ 1 (exp (* -2 x)))
17.0ms	(/ 2 (+ 1 (exp (* -2 x))))
86.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series134.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(+ 1 (exp (* -2 x)))
44.0ms	(/ 2 (+ 1 (exp (* -2 x))))
72.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify1.7s

Counts

159 → 159

Iterations

Iter	Nodes
done	5001
2	1439
1	443
0	183

prune495.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/15 x)
0.1b	(* (* x x) x)
18.4b	(fma (* (* x x) x) -1/3 (fma (pow x 5) 2/15 x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
5×	`add-sqr-sqrt`
4×	`*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-sqr` `fma-udef`
1×	`associate-l` `pow3` `*-commutative` `unswap-sqr`

Counts

3 → 53

Calls

3 calls:

1.0ms	(fma (pow x 5) 2/15 x)
28.0ms	(* (* x x) x)
0.0ms	(fma (* (* x x) x) -1/3 (fma (pow x 5) 2/15 x))

series315.0ms

Counts

3 → 9

Calls

3 calls:

195.0ms	(fma (pow x 5) 2/15 x)
53.0ms	(* (* x x) x)
68.0ms	(fma (* (* x x) x) -1/3 (fma (pow x 5) 2/15 x))

simplify1.3s

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
2	880
1	152
0	70

prune196.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1 (exp (* -2 x))))
0.0b	(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))
0.5b	(/ 2 (sqrt (+ 1 (exp (* -2 x)))))
2.7b	(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

1752×	`times-frac`
1504×	`*-un-lft-identity`
1059×	`add-sqr-sqrt`
1011×	`sqrt-prod`
996×	`add-cube-cbrt`
585×	`prod-diff`
249×	`distribute-lft-out`
195×	`fma-neg`
86×	`sqrt-div`
84×	`associate-/r/`
43×	`flip3-+` `flip-+`
42×	`div-inv`
30×	`associate-/l*`
17×	`add-exp-log`
14×	`associate-/r*` `difference-of-squares`
11×	`add-cbrt-cube`
7×	`difference-of-sqr-1` `div-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
3×	`expm1-def`
2×	`clear-num` `frac-2neg` `hypot-def`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `hypot-1-def` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 1133

Calls

4 calls:

19.0ms	(sqrt (+ 1 (exp (* -2 x))))
53.0ms	(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))
15.0ms	(/ 2 (sqrt (+ 1 (exp (* -2 x)))))
189.0ms	(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)

series243.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ 1 (exp (* -2 x))))
25.0ms	(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))
76.0ms	(/ 2 (sqrt (+ 1 (exp (* -2 x)))))
104.0ms	(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)

simplify2.2s

Counts

1145 → 1145

Iterations

Iter	Nodes
done	5000
1	1683
0	711

prune2.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ (sqrt 2) (+ 1 (exp (* -2 x))))
32.7b	(fma (/ (sqrt 2) 1) (/ (sqrt 2) (+ 1 (exp (* -2 x)))) -1)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`sqrt-prod`
8×	`distribute-lft-out`
6×	`associate-/l*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`associate-/r*`
3×	`expm1-log1p-u` `pow1` `fma-def` `insert-posit16` `log1p-expm1-u`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

3 → 80

Calls

3 calls:

9.0ms	(+ 1 (exp (* -2 x)))
11.0ms	(/ (sqrt 2) (+ 1 (exp (* -2 x))))
0.0ms	(fma (/ (sqrt 2) 1) (/ (sqrt 2) (+ 1 (exp (* -2 x)))) -1)

series271.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(+ 1 (exp (* -2 x)))
81.0ms	(/ (sqrt 2) (+ 1 (exp (* -2 x))))
169.0ms	(fma (/ (sqrt 2) 1) (/ (sqrt 2) (+ 1 (exp (* -2 x)))) -1)

simplify1.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5002
2	1175
1	303
0	133

prune465.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes403.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 30.9b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	30

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	1707×	body	1280	valid
527.0ms	1307×	body	640	valid
436.0ms	4052×	body	80	valid
287.0ms	617×	body	320	valid
54.0ms	317×	body	160	valid