Details

Time bar (total: 7.2s)

sample21.0ms

Algorithm
intervals
Results
7.0ms257×body80valid

simplify27.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (+ x y) x)

rewrite36.0ms

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:
35.0ms
(+ (+ x y) x)

series47.0ms

Counts
1 → 3
Calls
1 calls:
47.0ms
(+ (+ x y) x)

simplify1.6s

Counts
18 → 18

prune32.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (+ x y) x))
0.0b
(+ (+ x y) x)
0.0b
(+ (+ x y) x)
0.3b
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

rewrite345.0ms

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:
35.0ms
(sqrt (+ (+ x y) x))
29.0ms
(+ (+ x y) x)
44.0ms
(+ (+ x y) x)
233.0ms
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

series165.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(sqrt (+ (+ x y) x))
26.0ms
(+ (+ x y) x)
32.0ms
(+ (+ x y) x)
45.0ms
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

simplify543.0ms

Counts
128 → 128

prune242.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ (+ x y) x)))
0.1b
(sqrt (sqrt (+ (+ x y) x)))
0.3b
(* (sqrt (+ (+ x y) x)) (* (sqrt (sqrt (+ (+ x y) x))) (sqrt (sqrt (+ (+ x y) x)))))
0.3b
(* (sqrt (sqrt (+ (+ x y) x))) (sqrt (sqrt (+ (+ x y) x))))

rewrite618.0ms

Algorithm
rewrite-expression-head
Rules
141×sqrt-prod
122×sqrt-div
91×sqrt-pow1
81×*-un-lft-identity
69×pow1
60×add-sqr-sqrt
47×pow1/2
39×pow-prod-up
35×flip3-+ flip-+
33×distribute-lft-out
32×frac-times
25×swap-sqr
22×add-cube-cbrt
19×associate-*l*
16×associate-*r/
12×associate-*r* pow-prod-down
11×add-exp-log pow-sqr add-cbrt-cube unswap-sqr
10×associate-*l/
4×rem-sqrt-square prod-exp cbrt-unprod add-log-exp
3×sqrt-unprod
2×*-commutative
1×pow2 pow-plus rem-square-sqrt
Counts
4 → 215
Calls
4 calls:
35.0ms
(sqrt (sqrt (+ (+ x y) x)))
46.0ms
(sqrt (sqrt (+ (+ x y) x)))
328.0ms
(* (sqrt (+ (+ x y) x)) (* (sqrt (sqrt (+ (+ x y) x))) (sqrt (sqrt (+ (+ x y) x)))))
194.0ms
(* (sqrt (sqrt (+ (+ x y) x))) (sqrt (sqrt (+ (+ x y) x))))

series728.0ms

Counts
4 → 12
Calls
4 calls:
302.0ms
(sqrt (sqrt (+ (+ x y) x)))
309.0ms
(sqrt (sqrt (+ (+ x y) x)))
55.0ms
(* (sqrt (+ (+ x y) x)) (* (sqrt (sqrt (+ (+ x y) x))) (sqrt (sqrt (+ (+ x y) x)))))
62.0ms
(* (sqrt (sqrt (+ (+ x y) x))) (sqrt (sqrt (+ (+ x y) x))))

simplify1.3s

Counts
227 → 227

prune581.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify18.0ms

Counts
0 → 0

prune2.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify17.0ms

end0.0ms

sample818.0ms

Algorithm
intervals
Results
201.0ms8005×body80valid