Details

Time bar (total: 10.6s)

sample11.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
175
2105
3125
4135
done135

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (+ x y) x)

rewrite55.0ms

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:
54.0ms
(+ (+ x y) x)

series29.0ms

Counts
1 → 3
Calls
1 calls:
29.0ms
(+ (+ x y) x)

simplify3.4s

Counts
18 → 18
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
032145
180140
2239130
3813122
43728116
done5000116

prune51.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

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)))

rewrite306.0ms

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:
37.0ms
(sqrt (+ (+ x y) x))
55.0ms
(+ (+ x y) x)
30.0ms
(+ (+ x y) x)
180.0ms
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

series189.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(sqrt (+ (+ x y) x))
36.0ms
(+ (+ x y) x)
41.0ms
(+ (+ x y) x)
54.0ms
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

simplify2.1s

Counts
128 → 128
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01191813
12431227
26801143
321531053
done5000989

prune328.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×sqrt-prod
20×pow1
16×sqrt-div
13×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×flip3-+ swap-sqr flip-+
6×associate-*r* associate-*l*
5×add-exp-log pow-prod-up add-cbrt-cube
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr add-log-exp
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
3 → 87
Calls
3 calls:
19.0ms
(sqrt (+ (* 2 x) y))
10.0ms
(sqrt (+ (* 2 x) y))
74.0ms
(* (sqrt (+ (* 2 x) y)) (sqrt (+ (* 2 x) y)))

series216.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(sqrt (+ (* 2 x) y))
77.0ms
(sqrt (+ (* 2 x) y))
68.0ms
(* (sqrt (+ (* 2 x) y)) (sqrt (+ (* 2 x) y)))

simplify2.9s

Counts
96 → 96
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01071533
12281027
2613957
31654909
done5000889

prune245.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize7.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune4.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
077
1115
done115

end0.0ms

sample513.0ms

Algorithm
intervals
Results
278.0ms8005×body80valid