Details

Time bar (total: 10.1s)

sample10.0ms

Algorithm
intervals
Results
3.0ms256×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
045
165
295
3115
4125
done125

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize3.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (+ x y) x)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity add-log-exp
3×sum-log distribute-lft-out
1×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt associate-+l+ flip3-+ add-cbrt-cube flip-+
Counts
1 → 15
Calls
1 calls:
17.0ms
(+ (+ x y) x)

series21.0ms

Counts
1 → 3
Calls
1 calls:
21.0ms
(+ (+ x y) x)

simplify1.4s

Counts
18 → 18
Iterations

Useful iterations: 4 (280.0ms)

IterNodesCost
032145
189140
2218130
3642122
42639116
done5000116

prune25.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (+ x y) x))
0.0b
(+ (+ x y) x)
0.0b
(+ (+ x y) x)
0.2b
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
43×sqrt-prod
33×distribute-lft-out
26×add-sqr-sqrt
20×pow1
16×swap-sqr
14×sqrt-div add-log-exp
13×add-cube-cbrt
9×sqrt-pow1 flip3-+ pow1/2 flip-+
8×associate-*r* associate-*l*
6×add-exp-log sum-log add-cbrt-cube
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×+-commutative associate-+l+ associate-*r/ associate-*l/
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 116
Calls
4 calls:
17.0ms
(sqrt (+ (+ x y) x))
16.0ms
(+ (+ x y) x)
14.0ms
(+ (+ x y) x)
78.0ms
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

series118.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(sqrt (+ (+ x y) x))
21.0ms
(+ (+ x y) x)
24.0ms
(+ (+ x y) x)
35.0ms
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

simplify4.4s

Counts
128 → 128
Iterations

Useful iterations: 3 (548.0ms)

IterNodesCost
01191813
12551233
28681143
349121053
done50001053

prune172.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (* 2 x) y))
0.0b
(sqrt (+ (+ x y) x))
0.0b
(+ (+ x y) x)
0.2b
(* (sqrt (+ (+ x y) x)) (* 1 (sqrt (+ (* 2 x) y))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
16×sqrt-div
13×sqrt-prod
11×pow1 add-exp-log
10×add-sqr-sqrt
9×flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
8×add-cube-cbrt associate-*r/ associate-*l*
5×prod-exp
4×frac-times
3×pow-prod-down sum-log cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/
1×+-commutative associate-+l+ 1-exp associate-*r* *-commutative
Counts
4 → 79
Calls
4 calls:
4.0ms
(sqrt (+ (* 2 x) y))
19.0ms
(sqrt (+ (+ x y) x))
14.0ms
(+ (+ x y) x)
53.0ms
(* (sqrt (+ (+ x y) x)) (* 1 (sqrt (+ (* 2 x) y))))

series132.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(sqrt (+ (* 2 x) y))
40.0ms
(sqrt (+ (+ x y) x))
20.0ms
(+ (+ x y) x)
34.0ms
(* (sqrt (+ (+ x y) x)) (* 1 (sqrt (+ (* 2 x) y))))

simplify3.2s

Counts
91 → 91
Iterations

Useful iterations: 3 (484.0ms)

IterNodesCost
01431365
13621154
210661098
34408891
done5000891

prune200.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune1.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
067
1105
2125
done125

end0.0ms

sample226.0ms

Algorithm
intervals
Results
111.0ms8006×body80valid