Details

sample98.0ms

Algorithm

intervals

Results

56.0ms	62×	body	10240	exit
21.0ms	259×	body	80	valid
4.0ms	8×	body	640	valid
3.0ms	3×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log1p (exp x)) (* y x))
0.5b	(log1p (exp x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
35×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`add-cube-cbrt`
10×	`associate-l`
9×	`associate-r`
5×	`add-log-exp`
4×	`unswap-sqr`
3×	`expm1-log1p-u` `fma-neg` `*-commutative`
2×	`pow1` `log1p-udef` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `log1p-expm1` `flip--`

Counts

2 → 71

Calls

2 calls:

33.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series118.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (log1p (exp x)) (* y x))
55.0ms	(log1p (exp x))

simplify3.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
3	2407
2	735
1	333
0	146

prune200.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
35×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`add-cube-cbrt`
10×	`associate-l`
9×	`associate-r`
4×	`add-log-exp` `unswap-sqr`
3×	`fma-neg` `*-commutative`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

2 → 70

Calls

2 calls:

24.0ms	(- (fma x (fma 1/8 x 1/2) (log 2)) (* y x))
0.0ms	(fma x (fma 1/8 x 1/2) (log 2))

series89.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (fma x (fma 1/8 x 1/2) (log 2)) (* y x))
33.0ms	(fma x (fma 1/8 x 1/2) (log 2))

simplify2.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	3071
2	759
1	340
0	144

prune441.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (* (exp (* (fma 1/8 x 1/2) x)) 2)) (* y x))
0.0b	(* (fma 1/8 x 1/2) x)
0.5b	(log (* (exp (* (fma 1/8 x 1/2) x)) 2))

rewrite749.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt` `prod-diff`
53×	`pow1`
47×	`*-un-lft-identity`
39×	`add-cube-cbrt`
32×	`log-pow`
27×	`associate-l`
24×	`log-prod` `associate-r`
17×	`pow-prod-down`
12×	`associate--l+`
9×	`add-exp-log` `unswap-sqr`
8×	`*-commutative`
6×	`distribute-lft-out--` `add-log-exp`
5×	`add-cbrt-cube` `fma-neg`
3×	`expm1-log1p-u` `rem-log-exp` `prod-exp` `insert-posit16` `log1p-expm1-u`
2×	`diff-log` `difference-of-squares`
1×	`sub-neg` `flip3--` `cbrt-unprod` `flip--`

Counts

3 → 149

Calls

3 calls:

640.0ms	(- (log (* (exp (* (fma 1/8 x 1/2) x)) 2)) (* y x))
8.0ms	(* (fma 1/8 x 1/2) x)
91.0ms	(log (* (exp (* (fma 1/8 x 1/2) x)) 2))

series319.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(- (log (* (exp (* (fma 1/8 x 1/2) x)) 2)) (* y x))
97.0ms	(* (fma 1/8 x 1/2) x)
133.0ms	(log (* (exp (* (fma 1/8 x 1/2) x)) 2))

simplify1.9s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	1153
1	490
0	218

prune554.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x (fma 1/8 x 1/2) (log (sqrt 2)))
0.0b	(+ (fma x (fma 1/8 x 1/2) (log (sqrt 2))) (log (sqrt 2)))
1.0b	(log (sqrt 2))
1.0b	(log (sqrt 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`log-prod`
14×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`pow1` `sqrt-prod`
7×	`log-pow` `add-log-exp`
6×	`associate-+r+` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `fma-udef` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Counts

4 → 78

Calls

4 calls:

1.0ms	(fma x (fma 1/8 x 1/2) (log (sqrt 2)))
18.0ms	(+ (fma x (fma 1/8 x 1/2) (log (sqrt 2))) (log (sqrt 2)))
3.0ms	(log (sqrt 2))
2.0ms	(log (sqrt 2))

series142.0ms

Counts

4 → 8

Calls

4 calls:

54.0ms	(fma x (fma 1/8 x 1/2) (log (sqrt 2)))
88.0ms	(+ (fma x (fma 1/8 x 1/2) (log (sqrt 2))) (log (sqrt 2)))
0.0ms	(log (sqrt 2))
0.0ms	(log (sqrt 2))

simplify4.1s

Counts

86 → 86

Iterations

Iter	Nodes
done	5002
3	2371
2	429
1	162
0	85

prune450.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes77.0ms

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
done	7
1	7
0	6

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.6s	2288×	body	10240	exit
908.0ms	8318×	body	80	valid
142.0ms	262×	body	640	valid
141.0ms	147×	body	1280	valid
64.0ms	186×	body	320	valid
25.0ms	108×	body	160	valid