Details

sample115.0ms

Algorithm

intervals

Results

63.0ms	64×	body	10240	exit
29.0ms	270×	body	80	valid
5.0ms	7×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	5×	body	160	valid
1.0ms	1×	body	1280	valid

simplify10.0ms

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 2 expressions with local error:

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

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

series148.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(log1p (exp x))
83.0ms	(- (log1p (exp x)) (* y x))

simplify3.1s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
4	3665
3	987
2	327
1	129
0	61

prune190.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* y x) (* y x))
0.5b	(fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x))))
0.7b	(* (log1p (exp x)) (log1p (exp x)))
14.7b	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* y x) (* (* y x) (* y x)))) (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x)))))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

30.0ms	(* (* y x) (* y x))
0.0ms	(fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x))))
7.0ms	(* (log1p (exp x)) (log1p (exp x)))
275.0ms	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* y x) (* (* y x) (* y x)))) (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x)))))

series590.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* y x) (* y x))
154.0ms	(fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x))))
115.0ms	(* (log1p (exp x)) (log1p (exp x)))
286.0ms	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* y x) (* (* y x) (* y x)))) (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x)))))

simplify2.1s

Counts

125 → 125

Iterations

Iter	Nodes
done	5001
2	1507
1	447
0	171

prune658.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (log1p (exp x)) (log1p (exp x)))
10.1b	(sqrt (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x)))))
10.1b	(sqrt (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x)))))
10.7b	(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x))))))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
13×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

14.0ms	(* (log1p (exp x)) (log1p (exp x)))
3.0ms	(sqrt (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x)))))
2.0ms	(sqrt (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x)))))
265.0ms	(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x))))))

series903.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (log1p (exp x)) (log1p (exp x)))
210.0ms	(sqrt (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x)))))
186.0ms	(sqrt (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x)))))
419.0ms	(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (fma (log1p (exp x)) (log1p (exp x)) (fma (* y x) (log1p (exp x)) (* (* y x) (* y x))))))

simplify1.9s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	1074
1	352
0	146

prune774.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (exp x))
0.0b	(/ (+ 1 (exp x)) (exp (* y x)))
0.0b	(exp (* y x))
1.5b	(log (/ (+ 1 (exp x)) (exp (* y x))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
24×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
8×	`distribute-lft-out` `add-log-exp`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `fma-def`
2×	`flip3-+` `div-exp` `rem-log-exp` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `log-div` `exp-prod` `clear-num` `sum-log` `frac-2neg` `exp-to-pow` `log-pow` `rem-exp-log`

Counts

4 → 97

Calls

4 calls:

11.0ms	(+ 1 (exp x))
42.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
8.0ms	(exp (* y x))
12.0ms	(log (/ (+ 1 (exp x)) (exp (* y x))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1 (exp x))
34.0ms	(/ (+ 1 (exp x)) (exp (* y x)))
18.0ms	(exp (* y x))
52.0ms	(log (/ (+ 1 (exp x)) (exp (* y x))))

simplify3.3s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
3	2312
2	732
1	301
0	134

prune474.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes58.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	7
1	7
0	6

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.1s	2443×	body	10240	exit
820.0ms	8407×	body	80	valid
511.0ms	254×	body	640	valid
159.0ms	206×	body	320	valid
145.0ms	141×	body	1280	valid
16.0ms	80×	body	160	valid