Details

sample152.0ms

Algorithm

intervals

Results

91.0ms	79×	body	10240	exit
28.0ms	257×	body	80	valid
7.0ms	11×	body	640	valid
4.0ms	3×	body	1280	valid
3.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify46.0ms

Counts: 1 → 1

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 2 expressions with local error:

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

Slowest

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

series121.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

67.0ms	(log1p (exp x))
54.0ms	(- (log1p (exp x)) (* y x))

simplify2.6s

Counts: 40 → 40

prune328.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (sqrt (- (log1p (exp x)) (* y x))) (sqrt (- (log1p (exp x)) (* y x))))
0.5b	(sqrt (- (log1p (exp x)) (* y x)))
0.5b	(sqrt (- (log1p (exp x)) (* y x)))
0.5b	(log1p (exp x))

rewrite47.0ms

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:

Slowest

22.0ms	(* (sqrt (- (log1p (exp x)) (* y x))) (sqrt (- (log1p (exp x)) (* y x))))
11.0ms	(sqrt (- (log1p (exp x)) (* y x)))
11.0ms	(sqrt (- (log1p (exp x)) (* y x)))
1.0ms	(log1p (exp x))

series411.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(sqrt (- (log1p (exp x)) (* y x)))
116.0ms	(sqrt (- (log1p (exp x)) (* y x)))
80.0ms	(* (sqrt (- (log1p (exp x)) (* y x))) (sqrt (- (log1p (exp x)) (* y x))))
78.0ms	(log1p (exp x))

simplify854.0ms

Counts: 120 → 120

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

70×	`sqrt-div`
48×	`cbrt-div`
46×	`add-sqr-sqrt`
40×	`cbrt-prod`
35×	`flip3--` `flip--`
32×	`frac-times`
30×	`sqrt-prod`
20×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-*r/`
15×	`associate-l`
11×	`swap-sqr` `add-exp-log` `unswap-sqr`
10×	`pow1/3` `associate-r` `associate-*l/`
7×	`add-cbrt-cube`
5×	`pow-prod-down` `pow-prod-up`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative`
1×	`pow2` `pow-plus`

Counts

4 → 157

Calls

4 calls:

Slowest

73.0ms	(* (sqrt (- (log1p (exp x)) (* y x))) (* (cbrt (sqrt (- (log1p (exp x)) (* y x)))) (cbrt (sqrt (- (log1p (exp x)) (* y x))))))
23.0ms	(* (cbrt (sqrt (- (log1p (exp x)) (* y x)))) (cbrt (sqrt (- (log1p (exp x)) (* y x)))))
11.0ms	(sqrt (- (log1p (exp x)) (* y x)))
10.0ms	(sqrt (- (log1p (exp x)) (* y x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

481.0ms	(* (sqrt (- (log1p (exp x)) (* y x))) (* (cbrt (sqrt (- (log1p (exp x)) (* y x)))) (cbrt (sqrt (- (log1p (exp x)) (* y x))))))
346.0ms	(* (cbrt (sqrt (- (log1p (exp x)) (* y x)))) (cbrt (sqrt (- (log1p (exp x)) (* y x)))))
165.0ms	(sqrt (- (log1p (exp x)) (* y x)))
136.0ms	(sqrt (- (log1p (exp x)) (* y x)))

simplify1.5s

Counts: 169 → 169

prune2.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 2 expressions with local error:

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

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:

Slowest

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

series97.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

63.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
34.0ms	(fma x (fma x 1/8 1/2) (log 2))

simplify3.9s

Counts: 39 → 39

prune430.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes118.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.8s	2463×	body	10240	exit
1.0s	8407×	body	80	valid
151.0ms	260×	body	640	valid
125.0ms	132×	body	1280	valid
94.0ms	187×	body	320	valid
26.0ms	107×	body	160	valid