Details

sample53.0ms

Algorithm

intervals

Results

24.0ms	62×	body	10240	exit
9.0ms	261×	body	80	valid
3.0ms	5×	body	1280	valid
3.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	19	9
3	23	9
done	23	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.5b	(log (+ 1.0 (exp x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

7.0ms	(+ 1.0 (exp x))
13.0ms	(- (log (+ 1.0 (exp x))) (* x y))
6.0ms	(log (+ 1.0 (exp x)))

series139.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
65.0ms	(- (log (+ 1.0 (exp x))) (* x y))
66.0ms	(log (+ 1.0 (exp x)))

simplify2.2s

Counts

71 → 71

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	105	724
1	237	686
2	579	635
3	1589	618
4	3745	590
done	5000	589

prune171.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
7.8b	(log (fma (fma 1/2 x 1) x 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

12.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
1.0ms	(log (fma (fma 1/2 x 1) x 2.0))

series138.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(- (log (fma (fma 1/2 x 1) x 2.0)) (* x y))
54.0ms	(log (fma (fma 1/2 x 1) x 2.0))

simplify2.4s

Counts

45 → 45

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	93	722
1	222	681
2	564	626
3	1582	596
4	3752	567
done	5000	566

prune123.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (expm1 (log1p (log (fma (fma 1/2 x 1) x 2.0)))) (* x y))
0.0b	(log1p (log (fma (fma 1/2 x 1) x 2.0)))
0.3b	(expm1 (log1p (log (fma (fma 1/2 x 1) x 2.0))))
7.8b	(log (fma (fma 1/2 x 1) x 2.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

6.0ms	(- (expm1 (log1p (log (fma (fma 1/2 x 1) x 2.0)))) (* x y))
0.0ms	(log1p (log (fma (fma 1/2 x 1) x 2.0)))
0.0ms	(expm1 (log1p (log (fma (fma 1/2 x 1) x 2.0))))
2.0ms	(log (fma (fma 1/2 x 1) x 2.0))

series595.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(- (expm1 (log1p (log (fma (fma 1/2 x 1) x 2.0)))) (* x y))
123.0ms	(log1p (log (fma (fma 1/2 x 1) x 2.0)))
190.0ms	(expm1 (log1p (log (fma (fma 1/2 x 1) x 2.0))))
53.0ms	(log (fma (fma 1/2 x 1) x 2.0))

simplify1.9s

Counts

69 → 69

Iterations

Useful iterations: 3 (885.0ms)

Iter	Nodes	Cost
0	170	1316
1	427	1148
2	1278	1069
3	4762	1006
done	5000	1006

prune238.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0)))) (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0)))))
0.3b	(expm1 (* (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0)))) (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0))))))
7.8b	(log (fma (fma 1/2 x 1) x 2.0))
7.8b	(log (fma (fma 1/2 x 1) x 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`pow1`
18×	`sqrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `swap-sqr`
6×	`log-prod` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-log-exp` `log-pow`
1×	`pow2` `expm1-log1p` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `expm1-udef`

Counts

4 → 90

Calls

4 calls:

13.0ms	(* (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0)))) (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0)))))
0.0ms	(expm1 (* (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0)))) (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0))))))
1.0ms	(log (fma (fma 1/2 x 1) x 2.0))
1.0ms	(log (fma (fma 1/2 x 1) x 2.0))

series466.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0)))) (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0)))))
173.0ms	(expm1 (* (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0)))) (sqrt (log1p (log (fma (fma 1/2 x 1) x 2.0))))))
52.0ms	(log (fma (fma 1/2 x 1) x 2.0))
58.0ms	(log (fma (fma 1/2 x 1) x 2.0))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	165	2372
1	367	1617
2	1083	1423
3	4019	1331
done	5000	1328

prune330.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes74.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	10	9
done	10	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

911.0ms	2339×	body	10240	exit
307.0ms	8362×	body	80	valid
71.0ms	278×	body	640	valid
68.0ms	139×	body	1280	valid
30.0ms	200×	body	320	valid
9.0ms	97×	body	160	valid