Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	270×	pre	80	false

simplify10.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	47	11
3	107	11
4	238	11
5	625	11
6	3257	11
done	5001	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
26.2b	(/ (* b b) (* a a))

rewrite7.0ms

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×	`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 → 34

Calls

2 calls:

1.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
5.0ms	(/ (* b b) (* a a))

series43.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
26.0ms	(/ (* b b) (* a a))

simplify3.8s

Counts

40 → 40

Iterations

Useful iterations: 3 (352.0ms)

Iter	Nodes	Cost
0	65	498
1	164	462
2	664	370
3	4769	355
done	5000	355

prune79.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
0.1b	(* b (/ b a))
12.4b	(/ (* b (/ b a)) a)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`times-frac` `associate-r`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-l` `associate-/r*` `sqrt-prod` `add-log-exp`
2×	`associate-*r/` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

3 → 69

Calls

3 calls:

1.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
7.0ms	(* b (/ b a))
5.0ms	(/ (* b (/ b a)) a)

series62.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
21.0ms	(* b (/ b a))
26.0ms	(/ (* b (/ b a)) a)

simplify553.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	113	789
1	281	734
2	1321	623
done	5000	623

prune171.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (- 1 (log (exp (/ (* b (/ b a)) a))))))
0.1b	(* b (/ b a))
5.4b	(log (exp (/ (* b (/ b a)) a)))
12.4b	(/ (* b (/ b a)) a)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
16×	`times-frac`
13×	`associate-r`
8×	`pow1` `log-pow`
7×	`exp-prod`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`log-prod` `associate-l` `associate-/r*` `sqrt-prod` `div-inv`
2×	`associate-*r/` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-prod-down` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 88

Calls

4 calls:

1.0ms	(sqrt (fabs (- 1 (log (exp (/ (* b (/ b a)) a))))))
7.0ms	(* b (/ b a))
3.0ms	(log (exp (/ (* b (/ b a)) a)))
5.0ms	(/ (* b (/ b a)) a)

series87.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (fabs (- 1 (log (exp (/ (* b (/ b a)) a))))))
18.0ms	(* b (/ b a))
26.0ms	(log (exp (/ (* b (/ b a)) a)))
29.0ms	(/ (* b (/ b a)) a)

simplify576.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	141	1071
1	314	943
2	1374	798
done	5001	798

prune257.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	14	13
done	14	13

end0.0ms

sample599.0ms

Algorithm

intervals

Results

185.0ms	8000×	body	80	valid
95.0ms	8000×	pre	80	true
93.0ms	7828×	pre	80	false