Details

sample100.0ms

Algorithm

intervals

Results

39.0ms	519×	body	80	nan
28.0ms	239×	body	160	nan
16.0ms	256×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2004
8	2004
7	1307
6	580
5	196
4	68
3	37
2	21
1	17
0	7

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (fma x x -1)))
0.2b	(log (+ x (sqrt (fma x x -1))))
30.5b	(sqrt (fma x x -1))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `sqrt-prod` `insert-posit16` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

3 → 52

Calls

3 calls:

7.0ms	(+ x (sqrt (fma x x -1)))
5.0ms	(log (+ x (sqrt (fma x x -1))))
2.0ms	(sqrt (fma x x -1))

series293.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(+ x (sqrt (fma x x -1)))
168.0ms	(log (+ x (sqrt (fma x x -1))))
61.0ms	(sqrt (fma x x -1))

simplify812.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	2001
3	2001
2	742
1	268
0	119

prune289.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.2b	(/ 3/32 (* (* x x) (* x x)))
0.2b	(+ (log 2) (log x))
1.0b	(/ 1/4 (* x x))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
39×	`add-cbrt-cube` `add-exp-log`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
17×	`prod-exp` `cbrt-unprod`
15×	`*-un-lft-identity`
13×	`pow2`
11×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`cbrt-undiv` `div-exp`
6×	`log-prod` `times-frac` `associate-/l*`
5×	`log-pow`
4×	`expm1-log1p-u` `fma-def` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-+l+` `associate-+r+`
2×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

23.0ms	(* (* x x) (* x x))
24.0ms	(/ 3/32 (* (* x x) (* x x)))
6.0ms	(+ (log 2) (log x))
6.0ms	(/ 1/4 (* x x))

series534.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* x x) (* x x))
64.0ms	(/ 3/32 (* (* x x) (* x x)))
380.0ms	(+ (log 2) (log x))
51.0ms	(/ 1/4 (* x x))

simplify1.2s

Counts

160 → 160

Iterations

Iter	Nodes
done	2005
3	2005
2	1388
1	435
0	167

prune425.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (- x (+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))))
0.0b	(+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))
0.1b	(/ (/ 1/8 x) (* x x))
0.2b	(log (+ x (- x (+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x)))))

rewrite493.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
53×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`fma-def`
17×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`add-log-exp`
14×	`associate-+r+`
13×	`associate-/l*`
12×	`prod-diff` `distribute-lft-out`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`pow1` `sum-log` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `log-div` `diff-log` `prod-exp` `cbrt-unprod`
1×	`clear-num` `associate-+r-` `associate-/r*` `sub-neg` `frac-2neg` `rem-log-exp` `frac-add` `log-pow` `associate-/l/`

Counts

4 → 139

Calls

4 calls:

225.0ms	(+ x (- x (+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))))
50.0ms	(+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))
12.0ms	(/ (/ 1/8 x) (* x x))
204.0ms	(log (+ x (- x (+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x)))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ x (- x (+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))))
122.0ms	(+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))
47.0ms	(/ (/ 1/8 x) (* x x))
118.0ms	(log (+ x (- x (+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x)))))

simplify1.4s

Counts

151 → 151

Iterations

Iter	Nodes
done	2000
3	2000
2	1824
1	588
0	238

prune589.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.9s	8044×	body	160	nan
1.4s	16756×	body	80	nan
772.0ms	8000×	body	80	valid