Details

sample113.0ms

Algorithm

intervals

Results

60.0ms	66×	body	10240	exit
25.0ms	264×	body	80	valid
9.0ms	9×	body	1280	valid
4.0ms	7×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	26
3	26
2	22
1	15
0	8

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp x))
0.0b	(- (log (+ 1 (exp x))) (* x y))
0.5b	(log (+ 1 (exp x)))

rewrite46.0ms

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-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `log1p-def` `flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

3 → 66

Calls

3 calls:

10.0ms	(+ 1 (exp x))
16.0ms	(- (log (+ 1 (exp x))) (* x y))
19.0ms	(log (+ 1 (exp x)))

series156.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(+ 1 (exp x))
78.0ms	(- (log (+ 1 (exp x))) (* x y))
63.0ms	(log (+ 1 (exp x)))

simplify2.3s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	1600
2	609
1	223
0	97

prune303.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (+ 1 (exp x)))
0.2b	(sqrt (+ 1 (exp x)))
0.9b	(log (sqrt (+ 1 (exp x))))
0.9b	(log (sqrt (+ 1 (exp x))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`sqrt-prod`
14×	`log-prod`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `flip-+` `hypot-def` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `hypot-1-def`

Counts

4 → 90

Calls

4 calls:

13.0ms	(sqrt (+ 1 (exp x)))
10.0ms	(sqrt (+ 1 (exp x)))
5.0ms	(log (sqrt (+ 1 (exp x))))
5.0ms	(log (sqrt (+ 1 (exp x))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (+ 1 (exp x)))
32.0ms	(sqrt (+ 1 (exp x)))
144.0ms	(log (sqrt (+ 1 (exp x))))
151.0ms	(log (sqrt (+ 1 (exp x))))

simplify2.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
4	4987
3	1424
2	477
1	176
0	90

prune454.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log (fma (fma x 1/2 1) x 2)) (* x y))
6.3b	(log (fma (fma x 1/2 1) x 2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `log-prod` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`fma-neg` `prod-diff`
3×	`associate--l+` `add-exp-log` `log-pow` `add-log-exp`
2×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

2 → 41

Calls

2 calls:

10.0ms	(- (log (fma (fma x 1/2 1) x 2)) (* x y))
1.0ms	(log (fma (fma x 1/2 1) x 2))

series154.0ms

Counts

2 → 6

Calls

2 calls:

102.0ms	(- (log (fma (fma x 1/2 1) x 2)) (* x y))
52.0ms	(log (fma (fma x 1/2 1) x 2))

simplify2.1s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	1802
2	573
1	202
0	86

prune257.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (exp (log (log (fma (fma x 1/2 1) x 2)))) (* x y))
0.0b	(log (log (fma (fma x 1/2 1) x 2)))
0.3b	(exp (log (log (fma (fma x 1/2 1) x 2))))
6.3b	(log (fma (fma x 1/2 1) x 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

19×	`log-prod`
12×	`add-sqr-sqrt` `*-un-lft-identity` `exp-sum` `add-cube-cbrt`
11×	`pow1`
7×	`fma-neg` `prod-diff` `log-pow`
6×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`rem-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `rem-exp-log`

Counts

4 → 79

Calls

4 calls:

16.0ms	(- (exp (log (log (fma (fma x 1/2 1) x 2)))) (* x y))
1.0ms	(log (log (fma (fma x 1/2 1) x 2)))
3.0ms	(exp (log (log (fma (fma x 1/2 1) x 2))))
2.0ms	(log (fma (fma x 1/2 1) x 2))

series315.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (exp (log (log (fma (fma x 1/2 1) x 2)))) (* x y))
114.0ms	(log (log (fma (fma x 1/2 1) x 2)))
44.0ms	(exp (log (log (fma (fma x 1/2 1) x 2))))
52.0ms	(log (fma (fma x 1/2 1) x 2))

simplify2.8s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
3	3321
2	1068
1	359
0	158

prune514.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes125.0ms

Accuracy

0% (0.8b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	15
1	15
0	10

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.2s	2442×	body	10240	exit
1.2s	8461×	body	80	valid
160.0ms	241×	body	640	valid
125.0ms	139×	body	1280	valid
55.0ms	169×	body	320	valid
18.0ms	89×	body	160	valid