Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	220×	pre	80	false

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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: 15.6b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

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:

2.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
17.0ms	(/ (* b b) (* a a))

series71.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
43.0ms	(/ (* b b) (* a a))

simplify1.3s

Counts

44 → 44

Iterations

Useful iterations: 2 (561.0ms)

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

prune111.0ms

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)))

rewrite20.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 42

Calls

2 calls:

3.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
15.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

series30.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(sqrt (fabs (- 1 (* (fabs (/ b a)) (fabs (/ b a))))))
14.0ms	(* (fabs (/ b a)) (fabs (/ b a)))

simplify1.4s

Counts

48 → 48

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	55	633
1	116	456
2	899	405
done	5001	399

prune160.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

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)))

rewrite20.0ms

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×	`expm1-log1p-u` `pow-unpow` `log-prod` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u` `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 → 57

Calls

3 calls:

3.0ms	(sqrt (fabs (- 1 (log (exp (pow (fabs (/ b a)) 2))))))
5.0ms	(pow (fabs (/ b a)) 2)
9.0ms	(log (exp (pow (fabs (/ b a)) 2)))

series51.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(sqrt (fabs (- 1 (log (exp (pow (fabs (/ b a)) 2))))))
15.0ms	(pow (fabs (/ b a)) 2)
16.0ms	(log (exp (pow (fabs (/ b a)) 2)))

simplify1000.0ms

Counts

66 → 66

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	88	732
1	162	583
2	393	535
3	1274	535
done	5001	535

prune237.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample1.4s

Algorithm

intervals

Results

356.0ms	8000×	body	80	valid
186.0ms	8000×	pre	80	true
178.0ms	8130×	pre	80	false