Details

sample107.0ms

Algorithm

intervals

Results

57.0ms	81×	body	10240	exit
16.0ms	258×	body	80	valid
7.0ms	17×	body	640	valid
4.0ms	4×	body	1280	valid
2.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
3	23
2	19
1	12
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.7b	(log (+ 1.0 (exp x)))

rewrite408.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `log-prod` `add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`log-div` `fma-neg` `prod-diff` `associate--l+` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `add-cbrt-cube` `log-pow` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

3 → 62

Calls

3 calls:

396.0ms	(- (log (+ 1.0 (exp x))) (* x y))
5.0ms	(+ 1.0 (exp x))
5.0ms	(log (+ 1.0 (exp x)))

series193.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(- (log (+ 1.0 (exp x))) (* x y))
15.0ms	(+ 1.0 (exp x))
91.0ms	(log (+ 1.0 (exp x)))

simplify2.4s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	4578
2	827
1	243
0	105

prune424.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
0.7b	(log (+ 1.0 (exp x)))
0.7b	(log (+ 1.0 (exp x)))
0.7b	(log (+ 1.0 (exp x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`pow1` `log-prod`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
9×	`add-exp-log` `log-pow`
6×	`log-div` `add-cbrt-cube` `swap-sqr`
5×	`distribute-lft-out`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `flip-+`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

15.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
4.0ms	(log (+ 1.0 (exp x)))
4.0ms	(log (+ 1.0 (exp x)))
5.0ms	(log (+ 1.0 (exp x)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (log (+ 1.0 (exp x))) (log (+ 1.0 (exp x))))
83.0ms	(log (+ 1.0 (exp x)))
91.0ms	(log (+ 1.0 (exp x)))
93.0ms	(log (+ 1.0 (exp x)))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1295
1	239
0	94

prune538.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(+ 1.0 (exp x))
1.4b	(log (sqrt (+ 1.0 (exp x))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
14×	`log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`pow1` `sqrt-prod` `add-log-exp`
6×	`fma-def` `add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `sqrt-div` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp`

Counts

4 → 78

Calls

4 calls:

10.0ms	(+ 1.0 (exp x))
14.0ms	(+ 1.0 (exp x))
5.0ms	(log (sqrt (+ 1.0 (exp x))))
6.0ms	(log (sqrt (+ 1.0 (exp x))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ 1.0 (exp x))
9.0ms	(+ 1.0 (exp x))
129.0ms	(log (sqrt (+ 1.0 (exp x))))
114.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
done	5002
3	2373
2	505
1	167
0	84

prune673.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* x x) 1/2 (+ 2.0 x))
0.0b	(- (log (fma (* x x) 1/2 (+ 2.0 x))) (* x y))
7.1b	(log (fma (* x x) 1/2 (+ 2.0 x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `log-prod`
4×	`fma-neg` `prod-diff` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `associate--l+` `log-pow` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `fma-udef` `flip--`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma (* x x) 1/2 (+ 2.0 x))
12.0ms	(- (log (fma (* x x) 1/2 (+ 2.0 x))) (* x y))
2.0ms	(log (fma (* x x) 1/2 (+ 2.0 x)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(fma (* x x) 1/2 (+ 2.0 x))
118.0ms	(- (log (fma (* x x) 1/2 (+ 2.0 x))) (* x y))
59.0ms	(log (fma (* x x) 1/2 (+ 2.0 x)))

simplify2.8s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	4695
2	838
1	242
0	104

prune354.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes180.0ms

Accuracy

0% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 1.0b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.2s	2458×	body	10240	exit
567.0ms	8346×	body	80	valid
122.0ms	122×	body	1280	valid
105.0ms	261×	body	640	valid
51.0ms	196×	body	320	valid
17.0ms	113×	body	160	valid