Details

sample147.0ms

Algorithm

intervals

Results

82.0ms	96×	body	10240	exit
40.0ms	264×	body	80	valid
5.0ms	8×	body	640	valid
4.0ms	10×	body	320	valid
2.0ms	3×	body	1280	valid
1.0ms	5×	body	160	valid

simplify26.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

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:

Slowest

5.0ms	(- (log1p (exp x)) (* y x))
0.0ms	(log1p (exp x))

series107.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

54.0ms	(log1p (exp x))
53.0ms	(- (log1p (exp x)) (* y x))

simplify322.0ms

Counts: 44 → 40

prune331.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize60.0ms

Local error

Found 4 expressions with local error:

11.0b	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (fma (* y x) (fma x y (log1p (exp x))) (* (log1p (exp x)) (log1p (exp x)))))
0.7b	(* (log1p (exp x)) (log1p (exp x)))
0.7b	(* (log1p (exp x)) (log1p (exp x)))
0.5b	(log1p (exp x))

rewrite293.0ms

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:

Slowest

280.0ms	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (fma (* y x) (fma x y (log1p (exp x))) (* (log1p (exp x)) (log1p (exp x)))))
6.0ms	(* (log1p (exp x)) (log1p (exp x)))
6.0ms	(* (log1p (exp x)) (log1p (exp x)))
0.0ms	(log1p (exp x))

series396.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

190.0ms	(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (fma (* y x) (fma x y (log1p (exp x))) (* (log1p (exp x)) (log1p (exp x)))))
75.0ms	(* (log1p (exp x)) (log1p (exp x)))
66.0ms	(* (log1p (exp x)) (log1p (exp x)))
64.0ms	(log1p (exp x))

simplify606.0ms

Counts: 134 → 117

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

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:

Slowest

5.0ms	(- (fma x (* 1/8 x) (fma 1/2 x (log 2))) (* y x))
0.0ms	(fma x (* 1/8 x) (fma 1/2 x (log 2)))

series100.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

56.0ms	(- (fma x (* 1/8 x) (fma 1/2 x (log 2))) (* y x))
44.0ms	(fma x (* 1/8 x) (fma 1/2 x (log 2)))

simplify448.0ms

Counts: 44 → 39

prune333.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 3 expressions with local error:

36.8b	(posit16->real (real->posit16 (fma x (* 1/8 x) (fma 1/2 x (log 2)))))
0.0b	(fma x (* 1/8 x) (fma 1/2 x (log 2)))
0.0b	(- (posit16->real (real->posit16 (fma x (* 1/8 x) (fma 1/2 x (log 2))))) (* y x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

Slowest

5.0ms	(- (posit16->real (real->posit16 (fma x (* 1/8 x) (fma 1/2 x (log 2))))) (* y x))
0.0ms	(posit16->real (real->posit16 (fma x (* 1/8 x) (fma 1/2 x (log 2)))))
0.0ms	(fma x (* 1/8 x) (fma 1/2 x (log 2)))

series135.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

61.0ms	(- (posit16->real (real->posit16 (fma x (* 1/8 x) (fma 1/2 x (log 2))))) (* y x))
38.0ms	(posit16->real (real->posit16 (fma x (* 1/8 x) (fma 1/2 x (log 2)))))
36.0ms	(fma x (* 1/8 x) (fma 1/2 x (log 2)))

simplify462.0ms

Counts: 56 → 52

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes90.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.1s	2456×	body	10240	exit
1.3s	8388×	body	80	valid
166.0ms	259×	body	640	valid
101.0ms	124×	body	1280	valid
69.0ms	219×	body	320	valid
19.0ms	95×	body	160	valid