Details

sample95.0ms

Algorithm

intervals

Results

54.0ms	72×	body	10240	exit
22.0ms	275×	body	80	valid
4.0ms	6×	body	640	valid
2.0ms	6×	body	320	valid
2.0ms	1×	body	1280	valid
1.0ms	4×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	24
3	24
2	20
1	13
0	8

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log1p (exp x)) (* y x))
0.2b	(log1p (exp x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

11.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series139.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- (log1p (exp x)) (* y x))
69.0ms	(log1p (exp x))

simplify2.0s

Counts

40 → 40

Iterations

Iter	Nodes
4	2334
3	953
2	314
1	126
0	61

prune399.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
0.0b	(fma x (fma x 1/8 1/2) (log 2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

10.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
1.0ms	(fma x (fma x 1/8 1/2) (log 2))

series122.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
52.0ms	(fma x (fma x 1/8 1/2) (log 2))

simplify9.0s

Counts

39 → 39

Iterations

Iter	Nodes
4	8606
3	1766
2	343
1	130
0	59

prune348.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (exp x))
0.8b	(* (log1p (exp x)) (log1p (exp x)))
0.8b	(* (log1p (exp x)) (log1p (exp x)))
16.1b	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (fma (fma y x (log1p (exp x))) (* y x) (* (log1p (exp x)) (log1p (exp x)))))

rewrite344.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow3`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`expm1-log1p-u`
4×	`difference-cubes` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `log1p-udef` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `log1p-expm1` `div-inv` `flip--`

Counts

4 → 105

Calls

4 calls:

1.0ms	(log1p (exp x))
12.0ms	(* (log1p (exp x)) (log1p (exp x)))
11.0ms	(* (log1p (exp x)) (log1p (exp x)))
318.0ms	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (fma (fma y x (log1p (exp x))) (* y x) (* (log1p (exp x)) (log1p (exp x)))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(log1p (exp x))
107.0ms	(* (log1p (exp x)) (log1p (exp x)))
81.0ms	(* (log1p (exp x)) (log1p (exp x)))
241.0ms	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (fma (fma y x (log1p (exp x))) (* y x) (* (log1p (exp x)) (log1p (exp x)))))

simplify2.6s

Counts

117 → 117

Iterations

Iter	Nodes
3	4527
2	1075
1	340
0	136

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 1 expressions with local error:

0.0b	(* x (- (fma 1/8 x 1/2) y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
12×	`distribute-rgt-in` `distribute-lft-in`
5×	`associate-r`
3×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log`
2×	`sub-neg` `associate--l+` `associate-*r/` `fma-udef`
1×	`expm1-log1p-u` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `unswap-sqr`

Counts

1 → 49

Calls

1 calls:

32.0ms

(* x (- (fma 1/8 x 1/2) y))

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

(* x (- (fma 1/8 x 1/2) y))

simplify683.0ms

Counts

52 → 52

Iterations

Iter	Nodes
3	2092
2	490
1	216
0	116

prune369.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes63.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	7
1	7
0	6

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.3s	2504×	body	10240	exit
1.3s	8415×	body	80	valid
135.0ms	258×	body	640	valid
102.0ms	117×	body	1280	valid
57.0ms	176×	body	320	valid
23.0ms	116×	body	160	valid