Details

sample51.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true
5.0ms	220×	pre	80	false

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	47	11
3	100	11
4	319	11
5	1555	11
done	5000	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
33.2b	(/ (* b b) (* a a))

rewrite32.0ms

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:

2.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
28.0ms	(/ (* b b) (* a a))

series89.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
50.0ms	(/ (* b b) (* a a))

simplify1.2s

Counts

40 → 40

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	65	498
1	192	462
2	1613	378
done	5000	370

prune103.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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)))

rewrite16.0ms

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×	`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 → 38

Calls

2 calls:

2.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
12.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

series43.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
14.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

simplify1.2s

Counts

44 → 44

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	51	585
1	114	420
2	888	369
done	5000	363

prune124.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (- 1 (log (exp (pow (fabs (/ b a)) 2))))))
0.4b	(pow (fabs (/ b a)) 2)
7.0b	(log (exp (pow (fabs (/ b a)) 2)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `log-pow`
8×	`exp-prod`
6×	`pow1` `unpow-prod-down`
4×	`add-exp-log`
3×	`pow-unpow` `log-prod` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `rem-log-exp` `pow-exp`

Counts

3 → 51

Calls

3 calls:

1.0ms	(sqrt (fabs (- 1 (log (exp (pow (fabs (/ b a)) 2))))))
3.0ms	(pow (fabs (/ b a)) 2)
7.0ms	(log (exp (pow (fabs (/ b a)) 2)))

series34.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(sqrt (fabs (- 1 (log (exp (pow (fabs (/ b a)) 2))))))
9.0ms	(pow (fabs (/ b a)) 2)
9.0ms	(log (exp (pow (fabs (/ b a)) 2)))

simplify976.0ms

Counts

60 → 60

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	82	674
1	156	533
2	404	485
3	1159	485
done	5001	485

prune233.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	14	12
done	14	12

end0.0ms

sample1.8s

Algorithm

intervals

Results

618.0ms	8000×	pre	80	true
430.0ms	8000×	body	80	valid
152.0ms	8130×	pre	80	false