Details

sample59.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true
6.0ms	237×	pre	80	false

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	48	11
3	103	11
4	330	11
5	1613	11
done	5000	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
29.3b	(/ (* b b) (* a a))

rewrite17.0ms

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:

1.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
15.0ms	(/ (* b b) (* a a))

series61.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
43.0ms	(/ (* b b) (* a a))

simplify1.0s

Counts

44 → 44

Iterations

Useful iterations: 2 (209.0ms)

Iter	Nodes	Cost
0	69	538
1	193	502
2	1676	410
done	5001	410

prune138.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
13×	`swap-sqr` `associate-r` `associate-l`
10×	`pow1`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

2 → 84

Calls

2 calls:

3.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
44.0ms	(* (/ b a) (/ b a))

series81.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
60.0ms	(* (/ b a) (/ b a))

simplify2.3s

Counts

90 → 90

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	132	1119
1	416	1009
2	2822	912
done	5001	867

prune304.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
0.4b	(* (/ b a) (/ b a))
5.6b	(log (exp (* (/ b a) (/ b a))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`times-frac`
33×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-exp-log` `add-cbrt-cube`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
3×	`expm1-log1p-u` `log-prod` `sqrt-prod` `log-pow` `log1p-expm1-u`
1×	`pow2` `frac-times` `rem-sqrt-square` `exp-prod` `exp-to-pow` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

3 → 100

Calls

3 calls:

3.0ms	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
47.0ms	(* (/ b a) (/ b a))
8.0ms	(log (exp (* (/ b a) (/ b a))))

series136.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
48.0ms	(* (/ b a) (/ b a))
58.0ms	(log (exp (* (/ b a) (/ b a))))

simplify2.4s

Counts

109 → 109

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	151	1376
1	440	1187
2	2922	1072
done	5001	1023

prune399.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	12	13
done	12	13

end0.0ms

sample1.7s

Algorithm

intervals

Results

820.0ms	8000×	body	80	valid
189.0ms	8000×	pre	80	true
158.0ms	7780×	pre	80	false