Details

sample51.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
7.0ms	282×	pre	80	false
7.0ms	256×	pre	80	true

simplify5.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	48	11
3	101	11
4	198	11
5	376	11
6	618	11
7	1653	11
done	5001	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
34.6b	(/ (* b b) (* a a))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
4×	`cbrt-undiv` `add-sqr-sqrt` `div-exp` `prod-exp` `cbrt-unprod`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

2 → 38

Calls

2 calls:

3.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
15.0ms	(/ (* b b) (* a a))

series60.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
42.0ms	(/ (* b b) (* a a))

simplify9.8s

Counts

44 → 44

Iterations

Useful iterations: 4 (8.4s)

Iter	Nodes	Cost
0	69	538
1	148	502
2	492	410
3	1862	395
4	4721	385
done	5000	385

prune146.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
0.4b	(* (fabs (/ b a)) (fabs (/ b a)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

2 → 42

Calls

2 calls:

3.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
15.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

series44.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
17.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

simplify2.1s

Counts

48 → 48

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	55	633
1	87	453
2	186	405
3	410	389
4	1012	381
done	5001	377

prune180.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (fabs (- 1 (pow (fabs (/ b a)) 2))))
0.0b	(cbrt (fabs (- 1 (pow (fabs (/ b a)) 2))))
0.4b	(pow (fabs (/ b a)) 2)
0.4b	(pow (fabs (/ b a)) 2)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-prod` `unpow-prod-down` `pow-unpow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `unpow2` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

2.0ms	(cbrt (fabs (- 1 (pow (fabs (/ b a)) 2))))
2.0ms	(cbrt (fabs (- 1 (pow (fabs (/ b a)) 2))))
5.0ms	(pow (fabs (/ b a)) 2)
6.0ms	(pow (fabs (/ b a)) 2)

series181.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(cbrt (fabs (- 1 (pow (fabs (/ b a)) 2))))
94.0ms	(cbrt (fabs (- 1 (pow (fabs (/ b a)) 2))))
9.0ms	(pow (fabs (/ b a)) 2)
13.0ms	(pow (fabs (/ b a)) 2)

simplify2.0s

Counts

78 → 78

Iterations

Useful iterations: 4 (624.0ms)

Iter	Nodes	Cost
0	52	866
1	89	808
2	178	714
3	463	708
4	2131	704
done	5001	704

prune367.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	13
1	11	13
done	11	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

604.0ms	8000×	pre	80	true
370.0ms	8000×	body	80	valid
290.0ms	7938×	pre	80	false