Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	404
1	33	404
2	106	404
3	497	404
4	2870	404
done	5255	404

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
584×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`clear-num` `sum-log` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 463

Calls

4 calls:

28.0ms	(+ (+ alpha beta) (* beta alpha))
410.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
559.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
370.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (+ alpha beta) (* beta alpha))
165.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
225.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
135.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify5.0s

Counts

475 → 475

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	604	360265
1	1468	344492
2	4796	342247
done	5000	341967

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.4b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite806.0ms

Algorithm

rewrite-expression-head

Rules

112×	`sqrt-prod`
98×	`*-un-lft-identity`
84×	`times-frac`
68×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`associate-/l*`
12×	`associate-/r*` `sqrt-div`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 176

Calls

4 calls:

280.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
253.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
138.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
129.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series450.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
145.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
70.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
75.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify3.0s

Counts

188 → 188

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	160	106628
1	330	100062
2	899	99658
3	3452	99498
done	5008	99498

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.7b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.1b	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.5s

Algorithm

rewrite-expression-head

Rules

1930×	`times-frac`
1248×	`*-un-lft-identity`
945×	`add-sqr-sqrt`
777×	`sqrt-prod`
742×	`add-cube-cbrt`
258×	`associate-r`
243×	`distribute-lft-out`
193×	`associate-l`
104×	`associate-/r/`
71×	`associate-/l*`
54×	`flip3-+` `flip-+`
53×	`div-inv`
45×	`unswap-sqr`
27×	`add-exp-log`
22×	`add-cbrt-cube`
10×	`associate-/r*` `div-exp`
7×	`cbrt-undiv`
6×	`pow1` `prod-exp`
5×	`associate-/l/`
4×	`cbrt-unprod` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`1-exp`
1×	`frac-times` `sqrt-div` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 922

Calls

4 calls:

2.2s	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
429.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
359.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
383.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series655.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
159.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
137.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
125.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify8.5s

Counts

934 → 934

Iterations

Useful iterations: done (8.1s)

Iter	Nodes	Cost
0	1180	771189
1	3354	701127
done	5000	690034

prune6.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.7b

localize125.0ms

Local error

Found 4 expressions with local error:

3.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.4b	(sqrt (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite518.0ms

Algorithm

rewrite-expression-head

Rules

298×	`times-frac`
252×	`sqrt-prod`
188×	`*-un-lft-identity`
163×	`add-sqr-sqrt`
146×	`add-cube-cbrt`
86×	`cbrt-prod`
21×	`distribute-lft-out`
14×	`associate-/r/`
10×	`flip3-+` `flip-+`
7×	`rem-sqrt-square` `div-inv`
6×	`cbrt-div`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3` `sqrt-div`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 227

Calls

4 calls:

75.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
78.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
94.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
257.0ms	(sqrt (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

series661.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
104.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
85.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
374.0ms	(sqrt (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))

simplify1.1s

Iterations

Useful iterations: 0 (391.0ms)

Iter	Nodes	Cost
0	575	216094