Details

sample59.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
12.0ms	249×	pre	80	false
7.0ms	256×	pre	80	true

simplify4.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	47	11
3	98	11
4	187	11
5	332	11
6	498	11
7	1408	11
done	5001	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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)))))
23.0ms	(/ (* b b) (* a a))

series81.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
50.0ms	(/ (* b b) (* a a))

simplify10.3s

Counts

40 → 40

Iterations

Useful iterations: 4 (8.8s)

Iter	Nodes	Cost
0	65	498
1	145	462
2	488	370
3	1836	355
4	4570	345
done	5001	345

prune122.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (- 1 (exp (* (log (/ b a)) 2)))))
3.6b	(exp (* (log (/ b a)) 2))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `add-log-exp`
2×	`add-exp-log` `add-cbrt-cube`
1×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `sqrt-pow1` `pow1/2` `exp-lft-sqr` `rem-exp-log`

Counts

2 → 24

Calls

2 calls:

1.0ms	(sqrt (fabs (- 1 (exp (* (log (/ b a)) 2)))))
4.0ms	(exp (* (log (/ b a)) 2))

series52.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(sqrt (fabs (- 1 (exp (* (log (/ b a)) 2)))))
25.0ms	(exp (* (log (/ b a)) 2))

simplify2.3s

Counts

30 → 30

Iterations

Useful iterations: 4 (241.0ms)

Iter	Nodes	Cost
0	38	345
1	64	263
2	122	230
3	321	230
4	1026	228
done	5000	228

prune124.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (- 1 (log (exp (pow (/ b a) 2))))))
0.4b	(pow (/ b a) 2)
6.4b	(log (exp (pow (/ b a) 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

26×	`unpow-prod-down`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`log-pow`
18×	`exp-prod` `times-frac`
6×	`pow1` `add-exp-log`
3×	`pow-unpow` `log-prod` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
2×	`pow-exp` `div-inv` `unpow2` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp`

Counts

3 → 72

Calls

3 calls:

1.0ms	(sqrt (fabs (- 1 (log (exp (pow (/ b a) 2))))))
6.0ms	(pow (/ b a) 2)
19.0ms	(log (exp (pow (/ b a) 2)))

series108.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(sqrt (fabs (- 1 (log (exp (pow (/ b a) 2))))))
42.0ms	(pow (/ b a) 2)
34.0ms	(log (exp (pow (/ b a) 2)))

simplify1.3s

Counts

81 → 81

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	148	864
1	255	684
2	514	612
3	1530	611
done	5000	603

prune388.0ms

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	11	11
1	13	11
done	13	11

end0.0ms

sample1.5s

Algorithm

intervals

Results

508.0ms	8000×	body	80	valid
222.0ms	7897×	pre	80	false
170.0ms	8000×	pre	80	true