Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	265×	pre	80	false

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	47	11
3	97	11
4	179	11
5	293	11
6	459	11
7	1420	11
done	5000	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1 (/ (* b b) (* a a)))
0.0b	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
33.6b	(/ (* b b) (* a a))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `add-cube-cbrt` `div-exp` `prod-exp` `cbrt-unprod` `difference-of-squares`
3×	`times-frac` `sqrt-prod`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `clear-num` `associate-/r` `flip--` `div-inv` `associate-/l` `distribute-lft-out--`

Counts

3 → 51

Calls

3 calls:

4.0ms	(- 1 (/ (* b b) (* a a)))
1.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
5.0ms	(/ (* b b) (* a a))

series78.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(- 1 (/ (* b b) (* a a)))
15.0ms	(sqrt (fabs (- 1 (/ (* b b) (* a a)))))
29.0ms	(/ (* b b) (* a a))

simplify440.0ms

Counts

60 → 60

Iterations

Useful iterations: done (438.0ms)

Iter	Nodes	Cost
0	93	795
1	224	726
2	799	604
done	5002	587

prune117.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1 (/ (* b (/ b a)) a))
0.0b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
0.2b	(* b (/ b a))
15.7b	(/ (* b (/ b a)) a)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
15×	`add-cube-cbrt`
13×	`times-frac` `associate-r`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-l` `associate-/r*` `sqrt-prod`
2×	`associate-*r/` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip--` `associate-/l/` `associate-/l` `distribute-lft-out--`

Counts

4 → 84

Calls

4 calls:

4.0ms	(- 1 (/ (* b (/ b a)) a))
1.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
7.0ms	(* b (/ b a))
5.0ms	(/ (* b (/ b a)) a)

series96.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- 1 (/ (* b (/ b a)) a))
14.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
18.0ms	(* b (/ b a))
26.0ms	(/ (* b (/ b a)) a)

simplify679.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (150.0ms)

Iter	Nodes	Cost
0	137	1064
1	325	978
2	986	841
done	5000	841

prune203.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ (* b (/ b a)) a) 3)
0.4b	(* (/ b a) (/ b a))
15.7b	(/ (* b (/ b a)) a)
15.7b	(/ (* b (/ b a)) a)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
52×	`times-frac`
44×	`add-exp-log` `add-cbrt-cube`
41×	`add-cube-cbrt` `*-un-lft-identity`
16×	`cbrt-undiv` `div-exp`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
10×	`prod-exp` `cbrt-unprod`
8×	`div-inv`
7×	`unpow-prod-down` `cube-prod`
6×	`associate-/r*`
4×	`pow-exp` `add-log-exp` `rem-cube-cbrt` `unswap-sqr`
3×	`pow-unpow` `associate-*r/`
2×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`
1×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `pow-pow` `pow-plus` `unpow3` `pow-prod-down` `associate-l/` `pow-sqr` `-commutative` `pow-prod-up` `sqr-pow`

Counts

4 → 153

Calls

4 calls:

5.0ms	(pow (/ (* b (/ b a)) a) 3)
15.0ms	(* (/ b a) (/ b a))
5.0ms	(/ (* b (/ b a)) a)
5.0ms	(/ (* b (/ b a)) a)

series140.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (/ (* b (/ b a)) a) 3)
29.0ms	(* (/ b a) (/ b a))
26.0ms	(/ (* b (/ b a)) a)
26.0ms	(/ (* b (/ b a)) a)

simplify1.2s

Counts

165 → 165

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	181	1922
1	561	1563
2	2478	1369
done	5000	1348

prune437.0ms

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	16	33
1	22	33
done	22	33

end0.0ms

sample609.0ms

Algorithm

intervals

Results

191.0ms	8000×	body	80	valid
97.0ms	8000×	pre	80	true
91.0ms	7960×	pre	80	false