Details

sample54.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true
6.0ms	237×	pre	80	false

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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)))))
26.0ms	(/ (* b b) (* a a))

series72.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
35.0ms	(/ (* b b) (* a a))

simplify1.1s

Counts

40 → 40

Iterations

Useful iterations: done (1.1s)

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

prune123.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite62.0ms

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×	`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 → 80

Calls

2 calls:

3.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
52.0ms	(* (/ b a) (/ b a))

series67.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
46.0ms	(* (/ b a) (/ b a))

simplify2.6s

Counts

86 → 86

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	128	1079
1	415	969
2	2537	872
done	5000	827

prune235.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize11.0ms

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))))

rewrite60.0ms

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×	`log-prod` `sqrt-prod` `log-pow`
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 → 94

Calls

3 calls:

2.0ms	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
45.0ms	(* (/ b a) (/ b a))
4.0ms	(log (exp (* (/ b a) (/ b a))))

series99.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
30.0ms	(* (/ b a) (/ b a))
48.0ms	(log (exp (* (/ b a) (/ b a))))

simplify2.5s

Counts

103 → 103

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	145	1312
1	432	1131
2	2704	1016
done	5000	967

prune341.0ms

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	10	13
1	12	13
done	12	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

382.0ms	8000×	body	80	valid
224.0ms	7780×	pre	80	false
145.0ms	8000×	pre	80	true