Details

sample78.0ms

Algorithm

intervals

Results

44.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify1.5s

Counts: 1 → 1

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize58.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
0.0b	(+ (* alpha beta) (+ beta alpha))
0.0b	(+ (+ 1.0 (+ beta alpha)) 2)

rewrite603.0ms

Algorithm

rewrite-expression-head

Rules

3930×	`*-un-lft-identity`
2446×	`times-frac`
1990×	`distribute-lft-out`
691×	`add-sqr-sqrt` `add-cube-cbrt`
140×	`associate-/l*`
88×	`associate-/r/`
47×	`flip3-+` `flip-+`
44×	`div-inv`
18×	`add-log-exp`
15×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/r*`
9×	`sum-log`
7×	`cbrt-undiv` `div-exp`
4×	`pow1` `insert-posit16`
3×	`associate-/l/`
2×	`+-commutative` `clear-num` `frac-2neg`
1×	`associate-+l+` `associate-+r+`

Counts

4 → 1056

Calls

4 calls:

Slowest

269.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
172.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
70.0ms	(+ (+ 1.0 (+ beta alpha)) 2)
13.0ms	(+ (* alpha beta) (+ beta alpha))

series406.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

247.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 1.0 (+ beta alpha)) 2))
108.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
27.0ms	(+ (* alpha beta) (+ beta alpha))
24.0ms	(+ (+ 1.0 (+ beta alpha)) 2)

simplify1.4s

Counts: 1068 → 1068

prune11.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.9b

localize77.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
0.5b	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
0.1b	(/ (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
0.0b	(sqrt (+ (+ 1.0 (+ beta alpha)) 2))

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

65780×	`*-un-lft-identity`
47554×	`times-frac`
32695×	`distribute-lft-out`
16374×	`sqrt-prod`
13183×	`add-sqr-sqrt`
13182×	`add-cube-cbrt`
1370×	`associate-/l*`
1226×	`associate-/r/`
615×	`flip3-+` `flip-+`
613×	`div-inv`
29×	`add-cbrt-cube` `add-exp-log`
26×	`sqrt-div`
23×	`associate-/r*`
17×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`insert-posit16` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 13785

Calls

4 calls:

Slowest

540.0ms	(/ (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
365.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
139.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
71.0ms	(sqrt (+ (+ 1.0 (+ beta alpha)) 2))

series661.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

255.0ms	(/ (/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
234.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
120.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
53.0ms	(sqrt (+ (+ 1.0 (+ beta alpha)) 2))

simplify16.9s

Counts: 13797 → 13797

prune3.6m

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.9b

localize113.0ms

Local error

Found 4 expressions with local error:

3.8b	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
3.8b	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
1.6b	(* (/ (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) 1) 1) (/ (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))))
0.5b	(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))

rewrite49.3s

Algorithm

rewrite-expression-head

Rules

143078×	`*-un-lft-identity`
122814×	`times-frac`
71159×	`sqrt-prod`
66972×	`distribute-lft-out`
43629×	`add-sqr-sqrt`
34428×	`add-cube-cbrt`
25656×	`associate-r`
1726×	`associate-l`
1269×	`unswap-sqr`
1168×	`associate-/r/`
990×	`sqrt-div`
658×	`add-exp-log`
597×	`div-inv`
586×	`flip3-+` `flip-+`
566×	`div-exp`
316×	`associate-/l*`
163×	`add-cbrt-cube`
145×	`1-exp`
115×	`prod-exp`
106×	`cbrt-undiv`
25×	`cbrt-unprod`
9×	`associate-/r*`
8×	`pow1`
4×	`insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `associate-/l/`

Counts

4 → 32027

Calls

4 calls:

Slowest

46.1s	(* (/ (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) 1) 1) (/ (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))))
222.0ms	(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
81.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
65.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series409.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(* (/ (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) 1) 1) (/ (/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2))))
138.0ms	(/ (/ (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (sqrt (+ (+ 1.0 (+ beta alpha)) 2)))
65.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
51.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify1.3m

Counts: 32039 → 32039