Details

sample113.0ms

Algorithm

intervals

Results

65.0ms	68×	body	10240	exit
22.0ms	265×	body	80	valid
5.0ms	6×	body	1280	valid
4.0ms	8×	body	640	valid
1.0ms	5×	body	160	valid
1.0ms	3×	body	320	valid

simplify17.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log1p (exp x)) (* y x))
0.3b	(log1p (exp x))

rewrite11.0ms

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:

9.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series108.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (log1p (exp x)) (* y x))
59.0ms	(log1p (exp x))

simplify1.8s

Counts

40 → 40

Iterations

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

prune422.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(log1p (exp x))
0.5b	(sqrt (- (log1p (exp x)) (* y x)))
0.5b	(sqrt (- (log1p (exp x)) (* y x)))
0.6b	(* (sqrt (- (log1p (exp x)) (* y x))) (sqrt (- (log1p (exp x)) (* y x))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`flip3--` `swap-sqr` `flip--`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`expm1-log1p-u` `pow-prod-up`
4×	`frac-times` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `log1p-udef` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

1.0ms	(log1p (exp x))
9.0ms	(sqrt (- (log1p (exp x)) (* y x)))
5.0ms	(sqrt (- (log1p (exp x)) (* y x)))
35.0ms	(* (sqrt (- (log1p (exp x)) (* y x))) (sqrt (- (log1p (exp x)) (* y x))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(log1p (exp x))
159.0ms	(sqrt (- (log1p (exp x)) (* y x)))
159.0ms	(sqrt (- (log1p (exp x)) (* y x)))
65.0ms	(* (sqrt (- (log1p (exp x)) (* y x))) (sqrt (- (log1p (exp x)) (* y x))))

simplify4.2s

Counts

120 → 120

Iterations

Iter	Nodes
4	5991
3	1933
2	704
1	295
0	139

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (- (log1p (exp x)) (* y x)))
0.5b	(sqrt (- (log1p (exp x)) (* y x)))
0.5b	(sqrt (- (log1p (exp x)) (* y x)))
0.6b	(* (* (sqrt (sqrt (- (log1p (exp x)) (* y x)))) (sqrt (sqrt (- (log1p (exp x)) (* y x))))) (sqrt (- (log1p (exp x)) (* y x))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

96×	`sqrt-div`
60×	`sqrt-pow1`
51×	`pow1`
36×	`pow1/2`
34×	`pow-prod-up`
30×	`flip3--` `flip--`
28×	`frac-times`
16×	`add-sqr-sqrt`
14×	`associate-*l/` `sqrt-prod`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
8×	`associate-*r/` `pow-sqr`
7×	`pow-prod-down`
6×	`pow-plus` `associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-l` `*-commutative`

Counts

4 → 135

Calls

4 calls:

12.0ms	(sqrt (- (log1p (exp x)) (* y x)))
7.0ms	(sqrt (- (log1p (exp x)) (* y x)))
7.0ms	(sqrt (- (log1p (exp x)) (* y x)))
57.0ms	(* (* (sqrt (sqrt (- (log1p (exp x)) (* y x)))) (sqrt (sqrt (- (log1p (exp x)) (* y x))))) (sqrt (- (log1p (exp x)) (* y x))))

series587.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(sqrt (- (log1p (exp x)) (* y x)))
179.0ms	(sqrt (- (log1p (exp x)) (* y x)))
165.0ms	(sqrt (- (log1p (exp x)) (* y x)))
83.0ms	(* (* (sqrt (sqrt (- (log1p (exp x)) (* y x)))) (sqrt (sqrt (- (log1p (exp x)) (* y x))))) (sqrt (- (log1p (exp x)) (* y x))))

simplify1.7s

Counts

147 → 147

Iterations

Iter	Nodes
3	3262
2	1378
1	499
0	197

prune1.7s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

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:

0.0ms	(fma x (fma x 1/8 1/2) (log 2))
9.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))

series91.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(fma x (fma x 1/8 1/2) (log 2))
55.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))

simplify9.3s

Counts

39 → 39

Iterations

Iter	Nodes
4	9149
3	1737
2	353
1	129
0	59

prune423.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes101.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	7
1	7
0	6

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.5s	2415×	body	10240	exit
768.0ms	8387×	body	80	valid
132.0ms	266×	body	640	valid
128.0ms	138×	body	1280	valid
44.0ms	144×	body	320	valid
24.0ms	109×	body	160	valid