Details

sample134.0ms

Algorithm

intervals

Results

76.0ms	83×	body	10240	exit
26.0ms	263×	body	80	valid
6.0ms	10×	body	640	valid
5.0ms	5×	body	1280	valid
3.0ms	8×	body	320	valid
2.0ms	7×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

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

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

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))

series151.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(- (log1p (exp x)) (* y x))
71.0ms	(log1p (exp x))

simplify2.1s

Counts

40 → 40

Iterations

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

prune377.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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))

series138.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(- (log1p (exp x)) (* y x))
65.0ms	(log1p (exp x))

simplify2.0s

Counts

40 → 40

Iterations

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

prune363.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

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))

rewrite6.0ms

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))
5.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))

series116.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(fma x (fma x 1/8 1/2) (log 2))
66.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))

simplify8.8s

Counts

39 → 39

Iterations

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

prune362.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize81.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)))
1.4b	(fma (* y x) (fma x (fma 1/8 x 1/2) (log 2)) (fma (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)) (* (* y x) (* y x))))
3.4b	(- (* (fma x (fma 1/8 x 1/2) (log 2)) (* (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)))) (* (* (* y x) (* y x)) (* y x)))
19.9b	(/ (- (* (fma x (fma 1/8 x 1/2) (log 2)) (* (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)))) (* (* (* y x) (* y x)) (* y x))) (fma (* y x) (fma x (fma 1/8 x 1/2) (log 2)) (fma (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)) (* (* y x) (* y x)))))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
7×	`fma-udef`
6×	`add-log-exp`
5×	`distribute-rgt-in` `difference-cubes` `distribute-lft-in` `cube-unmult` `pow3`
4×	`expm1-log1p-u` `associate--l+` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `swap-sqr` `associate-r` `associate-l*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

10.0ms	(* (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)))
0.0ms	(fma (* y x) (fma x (fma 1/8 x 1/2) (log 2)) (fma (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)) (* (* y x) (* y x))))
72.0ms	(- (* (fma x (fma 1/8 x 1/2) (log 2)) (* (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)))) (* (* (* y x) (* y x)) (* y x)))
280.0ms	(/ (- (* (fma x (fma 1/8 x 1/2) (log 2)) (* (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)))) (* (* (* y x) (* y x)) (* y x))) (fma (* y x) (fma x (fma 1/8 x 1/2) (log 2)) (fma (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)) (* (* y x) (* y x)))))

series677.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)))
122.0ms	(fma (* y x) (fma x (fma 1/8 x 1/2) (log 2)) (fma (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)) (* (* y x) (* y x))))
186.0ms	(- (* (fma x (fma 1/8 x 1/2) (log 2)) (* (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)))) (* (* (* y x) (* y x)) (* y x)))
306.0ms	(/ (- (* (fma x (fma 1/8 x 1/2) (log 2)) (* (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)))) (* (* (* y x) (* y x)) (* y x))) (fma (* y x) (fma x (fma 1/8 x 1/2) (log 2)) (fma (fma x (fma 1/8 x 1/2) (log 2)) (fma x (fma 1/8 x 1/2) (log 2)) (* (* y x) (* y x)))))

simplify7.8s

Counts

112 → 112

Iterations

Iter	Nodes
3	11131
2	1873
1	529
0	208

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes109.0ms

Accuracy

0% (0.1b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	7
1	7
0	6

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.7s	2370×	body	10240	exit
913.0ms	8423×	body	80	valid
184.0ms	277×	body	640	valid
101.0ms	189×	body	320	valid
98.0ms	107×	body	1280	valid
20.0ms	93×	body	160	valid