Details

Time bar (total: 13.3s)

sample25.0ms

Algorithm
intervals
Results
14.0ms443×body80valid

simplify42.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
0715
11315
22313
3359
4439
5469
done469

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* y y))
0.1b
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
19×add-log-exp
10×sum-log
3×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ add-cbrt-cube flip-+
2×associate-+l+
Counts
3 → 38
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
31.0ms
(+ (+ (* x x) (* y y)) (* y y))
140.0ms
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series118.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* x x) (* y y))
41.0ms
(+ (+ (* x x) (* y y)) (* y y))
46.0ms
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify2.2s

Counts
47 → 47
Iterations

Useful iterations: 3 (855.0ms)

IterNodesCost
070791
1211667
2725591
32852513
done5000513

prune185.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(* 2 (pow y 2))
0.1b
(+ (+ (* x x) (* y y)) (* 2 (pow y 2)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-log-exp
8×add-exp-log associate-*r*
6×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down sum-log unswap-sqr
3×pow1 associate-*l* prod-exp
2×+-commutative flip3-+ flip-+ unpow2 sqr-pow
1×pow-to-exp associate-+l+ pow-exp *-commutative cbrt-unprod
Counts
3 → 51
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
23.0ms
(* 2 (pow y 2))
53.0ms
(+ (+ (* x x) (* y y)) (* 2 (pow y 2)))

series154.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(+ (* x x) (* y y))
56.0ms
(* 2 (pow y 2))
57.0ms
(+ (+ (* x x) (* y y)) (* 2 (pow y 2)))

simplify2.9s

Counts
60 → 60
Iterations

Useful iterations: done (2.9s)

IterNodesCost
098703
1262630
2775521
33061503
done5000486

prune206.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.1b
(+ (+ (* x x) (* y y)) (* (* y 2) (pow y (/ 2 2))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
4×sum-log
2×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ add-cbrt-cube flip-+
1×associate-+l+
Counts
2 → 24
Calls
2 calls:
8.0ms
(+ (* x x) (* y y))
53.0ms
(+ (+ (* x x) (* y y)) (* (* y 2) (pow y (/ 2 2))))

series94.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(+ (* x x) (* y y))
53.0ms
(+ (+ (* x x) (* y y)) (* (* y 2) (pow y (/ 2 2))))

simplify2.3s

Counts
30 → 30
Iterations

Useful iterations: 3 (848.0ms)

IterNodesCost
057551
1189477
2687373
33013337
done5000337

prune133.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
0.1b
(+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* (* y 2) (pow y (/ 2 2))))
6.1b
(sqrt (+ (* x x) (* y y)))
6.1b
(sqrt (+ (* x x) (* y y)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 98
Calls
4 calls:
50.0ms
(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
39.0ms
(+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* (* y 2) (pow y (/ 2 2))))
9.0ms
(sqrt (+ (* x x) (* y y)))
9.0ms
(sqrt (+ (* x x) (* y y)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))))
51.0ms
(+ (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (* (* y 2) (pow y (/ 2 2))))
58.0ms
(sqrt (+ (* x x) (* y y)))
57.0ms
(sqrt (+ (* x x) (* y y)))

simplify3.7s

Counts
110 → 110
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01112348
12571511
28821291
338791193
done50011171

prune455.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes3.0ms