Details

sample106.0ms

Algorithm

intervals

Results

33.0ms	260×	body	160	nan
28.0ms	510×	body	80	nan
25.0ms	256×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3303
5	365
4	73
3	38
2	23
1	17
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (fma x x -1))))
0.0b	(+ x (sqrt (fma x x -1)))
30.4b	(sqrt (fma x x -1))

rewrite11.0ms

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:

4.0ms	(log (+ x (sqrt (fma x x -1))))
5.0ms	(+ x (sqrt (fma x x -1)))
1.0ms	(sqrt (fma x x -1))

series317.0ms

Counts

3 → 9

Calls

3 calls:

191.0ms	(log (+ x (sqrt (fma x x -1))))
79.0ms	(+ x (sqrt (fma x x -1)))
47.0ms	(sqrt (fma x x -1))

simplify2.3s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
3	4953
2	901
1	269
0	119

prune314.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 (* x x)) x)))
0.0b	(- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 (* x x)) x))
0.1b	(/ (/ 1/8 (* x x)) x)
0.8b	(/ 1/8 (* x x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
107×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
91×	`add-cube-cbrt`
75×	`prod-diff`
19×	`add-exp-log`
18×	`add-cbrt-cube` `div-inv`
10×	`associate-/l*`
7×	`cbrt-undiv` `log-prod` `div-exp`
6×	`add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`log-div` `clear-num` `frac-2neg` `flip3--` `prod-exp` `cbrt-unprod` `flip--` `distribute-lft-out--`
1×	`sub-neg` `diff-log` `rem-log-exp` `associate--l+` `log-pow` `fma-udef` `associate-/l/`

Counts

4 → 194

Calls

4 calls:

19.0ms	(log (- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 (* x x)) x)))
19.0ms	(- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 (* x x)) x))
15.0ms	(/ (/ 1/8 (* x x)) x)
12.0ms	(/ 1/8 (* x x))

series244.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(log (- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 (* x x)) x)))
48.0ms	(- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 (* x x)) x))
41.0ms	(/ (/ 1/8 (* x x)) x)
30.0ms	(/ 1/8 (* x x))

simplify2.9s

Counts

206 → 206

Iterations

Iter	Nodes
done	5000
2	4943
1	994
0	389

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (log (+ x (sqrt (fma x x -1)))))
0.6b	(* (sqrt (log (+ x (sqrt (fma x x -1))))) (sqrt (log (+ x (sqrt (fma x x -1))))))
30.4b	(sqrt (fma x x -1))
30.4b	(sqrt (fma x x -1))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

36×	`sqrt-prod`
30×	`add-sqr-sqrt`
29×	`pow1`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`sqrt-pow1` `pow1/2` `swap-sqr`
7×	`associate-r` `associate-l` `log-pow`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `pow-prod-down` `pow-sqr`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 106

Calls

4 calls:

9.0ms	(sqrt (log (+ x (sqrt (fma x x -1)))))
10.0ms	(* (sqrt (log (+ x (sqrt (fma x x -1))))) (sqrt (log (+ x (sqrt (fma x x -1))))))
1.0ms	(sqrt (fma x x -1))
1.0ms	(sqrt (fma x x -1))

series539.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(sqrt (log (+ x (sqrt (fma x x -1)))))
175.0ms	(* (sqrt (log (+ x (sqrt (fma x x -1))))) (sqrt (log (+ x (sqrt (fma x x -1))))))
49.0ms	(sqrt (fma x x -1))
77.0ms	(sqrt (fma x x -1))

simplify2.1s

Counts

118 → 118

Iterations

Iter	Nodes
done	5001
2	1542
1	398
0	169

prune518.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
0	11

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.6s	15928×	body	80	nan
1.4s	7666×	body	160	nan
745.0ms	8000×	body	80	valid