Details

Time bar (total: 8.1s)

sample42.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
7.0ms256×pre80true

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 7 (767.0ms)

IterNodesCost
09282
122282
246282
395282
4177282
5339282
6575282
71519242
done5002242

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(- (/ (* x x) (+ (* x x) (* y y))) (/ (* y y) (+ (* x x) (* y y))))
16.2b
(/ (* x x) (+ (* x x) (* y y)))
26.6b
(/ (* y y) (+ (* x x) (* y y)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×add-cbrt-cube add-exp-log
10×*-un-lft-identity times-frac
8×associate-/r/ add-cube-cbrt add-log-exp
6×associate-/r*
5×flip3-+ flip-+
4×pow1 cbrt-undiv div-exp div-inv difference-of-squares
3×distribute-rgt-out--
2×clear-num frac-2neg prod-exp cbrt-unprod associate-/l*
1×+-commutative sum-log sub-neg flip3-- diff-log frac-sub flip-- distribute-lft-out-- sub-div
Counts
4 → 79
Calls
4 calls:
6.0ms
(+ (* x x) (* y y))
74.0ms
(- (/ (* x x) (+ (* x x) (* y y))) (/ (* y y) (+ (* x x) (* y y))))
13.0ms
(/ (* x x) (+ (* x x) (* y y)))
15.0ms
(/ (* y y) (+ (* x x) (* y y)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (* x x) (* y y))
93.0ms
(- (/ (* x x) (+ (* x x) (* y y))) (/ (* y y) (+ (* x x) (* y y))))
69.0ms
(/ (* x x) (+ (* x x) (* y y)))
82.0ms
(/ (* y y) (+ (* x x) (* y y)))

simplify2.7s

Counts
91 → 91
Iterations

Useful iterations: 2 (634.0ms)

IterNodesCost
012825493
142522421
2180322061
done500122061

prune489.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize1.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune26.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ y (sqrt (+ (* x x) (* y y)))) (/ y (sqrt (+ (* x x) (* y y)))))
16.2b
(/ (* x x) (+ (* x x) (* y y)))
22.3b
(sqrt (+ (* x x) (* y y)))
22.3b
(sqrt (+ (* x x) (* y y)))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
99×times-frac
64×*-un-lft-identity add-cube-cbrt
54×sqrt-prod
30×swap-sqr
24×associate-*r* associate-*l*
21×add-cbrt-cube add-exp-log
13×pow1
12×sqrt-div
10×associate-/r/
9×unswap-sqr
7×flip3-+ flip-+
6×cbrt-undiv div-exp
5×prod-exp cbrt-unprod div-inv
4×add-log-exp
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow2 frac-times clear-num frac-2neg pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up associate-/l*
Counts
4 → 164
Calls
4 calls:
67.0ms
(* (/ y (sqrt (+ (* x x) (* y y)))) (/ y (sqrt (+ (* x x) (* y y)))))
32.0ms
(/ (* x x) (+ (* x x) (* y y)))
12.0ms
(sqrt (+ (* x x) (* y y)))
12.0ms
(sqrt (+ (* x x) (* y y)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (/ y (sqrt (+ (* x x) (* y y)))) (/ y (sqrt (+ (* x x) (* y y)))))
73.0ms
(/ (* x x) (+ (* x x) (* y y)))
48.0ms
(sqrt (+ (* x x) (* y y)))
45.0ms
(sqrt (+ (* x x) (* y y)))

simplify260.0ms

Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
020764103