Details

sample71.0ms

Algorithm

intervals

Results

20.0ms	117×	body	320	valid
20.0ms	136×	body	160	valid
13.0ms	246×	body	80	nan
0.0ms	3×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	19	37
1	44	37
2	122	36
3	301	36
4	574	36
5	885	36
6	1154	36
7	1428	36
8	2979	36
done	5000	36

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize21.0ms

Local error

Found 4 expressions with local error:

6.5b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `frac-times` `sqrt-div` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `associate-*l/` `difference-of-squares`

Counts

4 → 68

Calls

4 calls:

17.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
20.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
5.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
304.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
43.0ms	(sqrt (- (* g g) (* h h)))
48.0ms	(sqrt (- (* g g) (* h h)))

simplify480.0ms

Counts

80 → 80

Iterations

Useful iterations: done (478.0ms)

Iter	Nodes	Cost
0	183	1500
1	412	1315
2	1429	1211
done	5000	1182

prune417.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 32.4b

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* g g) (* h h))
8.2b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
31.1b	(sqrt (- (* g g) (* h h)))
31.1b	(sqrt (- (* g g) (* h h)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `fma-neg` `pow1/3` `diff-log` `prod-diff` `associate-*l/`

Counts

4 → 69

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
21.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
7.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* g g) (* h h))
307.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
48.0ms	(sqrt (- (* g g) (* h h)))
46.0ms	(sqrt (- (* g g) (* h h)))

simplify367.0ms

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	144	1192
1	310	1048
2	1040	954