Details

sample69.0ms

Algorithm

intervals

Results

23.0ms	117×	body	320	valid
15.0ms	136×	body	160	valid
12.0ms	246×	body	80	nan
0.0ms	3×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	19	37
1	43	37
2	119	36
3	284	36
4	529	36
5	772	36
6	944	36
7	1144	36
8	2472	36
done	5000	36

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize18.0ms

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)))

rewrite43.0ms

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` `frac-times` `sqrt-div` `associate-*r/` `add-cbrt-cube` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `associate-*l/` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

15.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
18.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series727.0ms

Counts

4 → 12

Calls

4 calls:

308.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
325.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
44.0ms	(sqrt (- (* g g) (* h h)))
49.0ms	(sqrt (- (* g g) (* h h)))

simplify477.0ms

Counts

72 → 72

Iterations

Useful iterations: done (474.0ms)

Iter	Nodes	Cost
0	177	1390
1	392	1217
2	1357	1121
done	5000	1082

prune408.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 32.5b

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)))

rewrite33.0ms

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` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

3.0ms	(- (* g g) (* h h))
22.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
4.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* g g) (* h h))
320.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (sqrt (- (* g g) (* h h))) g)))
51.0ms	(sqrt (- (* g g) (* h h)))
45.0ms	(sqrt (- (* g g) (* h h)))

simplify311.0ms

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	135	1086
1	290	956
2	974	870