Details

sample82.0ms

Algorithm

intervals

Results

31.0ms	52×	body	1280	valid
16.0ms	39×	body	640	valid
12.0ms	136×	body	80	valid
5.0ms	17×	body	320	valid
2.0ms	12×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2017
8	2017
7	682
6	240
5	101
4	51
3	30
2	22
1	18
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
3.9b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite162.0ms

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:

12.0ms	(+ 1 (exp (* -2 x)))
24.0ms	(/ 2 (+ 1 (exp (* -2 x))))
122.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series134.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1 (exp (* -2 x)))
29.0ms	(/ 2 (+ 1 (exp (* -2 x))))
89.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify1.9s

Counts

159 → 159

Iterations

Iter	Nodes
done	2002
3	2002
2	930
1	426
0	183

prune585.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 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)))))
3.9b	(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

1752×	`times-frac`
1503×	`*-un-lft-identity`
1054×	`add-sqr-sqrt`
1007×	`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*`
17×	`add-exp-log`
14×	`associate-/r*` `difference-of-squares`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`difference-of-sqr-1` `div-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
3×	`expm1-def` `fma-def`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

4 → 1129

Calls

4 calls:

11.0ms	(+ 1 (exp (* -2 x)))
30.0ms	(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))
23.0ms	(/ 2 (sqrt (+ 1 (exp (* -2 x)))))
215.0ms	(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)

series206.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ 1 (exp (* -2 x)))
21.0ms	(/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x)))))
77.0ms	(/ 2 (sqrt (+ 1 (exp (* -2 x)))))
87.0ms	(- (/ (/ 2 (sqrt (+ 1 (exp (* -2 x))))) (sqrt (+ 1 (exp (* -2 x))))) 1)

simplify1.9s

Counts

1141 → 1141

Iterations

Iter	Nodes
done	2008
2	2008
1	1646
0	710

prune3.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/15 x)
0.1b	(* x (* x x))
17.9b	(fma -1/3 (* x (* x x)) (fma (pow x 5) 2/15 x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma (pow x 5) 2/15 x)
18.0ms	(* x (* x x))
0.0ms	(fma -1/3 (* x (* x x)) (fma (pow x 5) 2/15 x))

series387.0ms

Counts

3 → 9

Calls

3 calls:

223.0ms	(fma (pow x 5) 2/15 x)
70.0ms	(* x (* x x))
93.0ms	(fma -1/3 (* x (* x x)) (fma (pow x 5) 2/15 x))

simplify1.5s

Counts

58 → 58

Iterations

Iter	Nodes
done	2034
4	2034
3	1429
2	365
1	122
0	71

prune255.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes339.0ms

Accuracy

98.5% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 29.7b

bsearch2.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	1730×	body	1280	valid
859.0ms	1195×	body	640	valid
394.0ms	4112×	body	80	valid
241.0ms	627×	body	320	valid
60.0ms	336×	body	160	valid