Details

sample106.0ms

Algorithm

intervals

Results

35.0ms	510×	body	80	nan
29.0ms	235×	body	160	nan
18.0ms	256×	body	80	valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
8	3499
7	1307
6	580
5	196
4	68
3	37
2	21
1	17
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize14.0ms

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)))
32.5b	(sqrt (fma x x -1))

rewrite10.0ms

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))))
4.0ms	(+ x (sqrt (fma x x -1)))
2.0ms	(sqrt (fma x x -1))

series257.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(log (+ x (sqrt (fma x x -1))))
68.0ms	(+ x (sqrt (fma x x -1)))
60.0ms	(sqrt (fma x x -1))

simplify1.5s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
3	2305
2	739
1	268
0	119

prune253.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ -1/8 (* (* x x) x)) (/ 1/2 x))
0.0b	(log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
0.1b	(* (* x x) x)
0.4b	(/ -1/8 (* (* x x) x))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

109×	`times-frac`
91×	`add-sqr-sqrt` `prod-diff`
87×	`*-un-lft-identity`
85×	`add-cube-cbrt`
24×	`pow1`
22×	`div-inv`
19×	`add-exp-log`
18×	`add-cbrt-cube`
7×	`fma-neg`
6×	`pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `log-prod` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `pow-sqr` `difference-of-squares`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `flip3--` `diff-log` `rem-log-exp` `associate-l` `pow3` `log-pow` `-commutative` `frac-sub` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 189

Calls

4 calls:

55.0ms	(- (/ -1/8 (* (* x x) x)) (/ 1/2 x))
1.0ms	(log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
18.0ms	(* (* x x) x)
15.0ms	(/ -1/8 (* (* x x) x))

series274.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (/ -1/8 (* (* x x) x)) (/ 1/2 x))
101.0ms	(log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x))))
39.0ms	(* (* x x) x)
40.0ms	(/ -1/8 (* (* x x) x))

simplify1.7s

Counts

201 → 201

Iterations

Iter	Nodes
done	5001
2	2142
1	763
0	324

prune559.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ -1/8 (* (* x x) x))
0.4b	(/ -1/8 (* (* x x) x))
0.5b	(* (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x)))) (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
0.5b	(cbrt (* (* (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x)))) (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x))))) (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-cbrt-cube` `add-exp-log`
17×	`pow1`
16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
7×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `log-prod` `times-frac` `swap-sqr` `div-exp` `log-pow` `associate-/l*`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `pow3` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

13.0ms	(/ -1/8 (* (* x x) x))
14.0ms	(/ -1/8 (* (* x x) x))
10.0ms	(* (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x)))) (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
12.0ms	(cbrt (* (* (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x)))) (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x))))) (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x))))))

series341.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ -1/8 (* (* x x) x))
60.0ms	(/ -1/8 (* (* x x) x))
129.0ms	(* (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x)))) (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
92.0ms	(cbrt (* (* (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x)))) (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x))))) (log (fma 2 x (- (/ -1/8 (* (* x x) x)) (/ 1/2 x))))))

simplify1.9s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
2	1839
1	548
0	211

prune606.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	16024×	body	80	nan
1.0s	8000×	body	80	valid
949.0ms	7610×	body	160	nan