Details

Time bar (total: 11.6s)

sample33.0ms

Algorithm
intervals
Results
18.0ms256×body80valid

simplify299.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0919
11719
23519
36719
411119
515819
617319
717419
done17419

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* (* y 4.0) y))
4.7b
(- (* x x) (* (* y 4.0) y))
30.6b
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
9.0ms
(+ (* x x) (* (* y 4.0) y))
8.0ms
(- (* x x) (* (* y 4.0) y))
63.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series213.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(+ (* x x) (* (* y 4.0) y))
76.0ms
(- (* x x) (* (* y 4.0) y))
91.0ms
(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify3.0s

Counts
64 → 64
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0871404
12331375
27691233
328911226
done50011210

prune191.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize0.0ms

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

prune8.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* (* y 4.0) y))
0.0b
(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
4.7b
(- (* x x) (* (* y 4.0) y))
30.6b
(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
8×div-exp add-log-exp
6×flip3-- flip-- div-inv associate-/l*
5×pow1
4×cbrt-undiv
2×rec-exp frac-2neg flip3-+ 1-exp clear-num flip-+ associate-/l/
1×+-commutative sub-neg pow-flip diff-log sum-log inv-pow
Counts
4 → 138
Calls
4 calls:
9.0ms
(+ (* x x) (* (* y 4.0) y))
48.0ms
(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
8.0ms
(- (* x x) (* (* y 4.0) y))
53.0ms
(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(+ (* x x) (* (* y 4.0) y))
89.0ms
(/ 1 (/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
69.0ms
(- (* x x) (* (* y 4.0) y))
82.0ms
(/ (+ (* x x) (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

simplify3.4s

Counts
150 → 150
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01924490
14474224
211583827
341883710
done50013710

prune444.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

localize29.0ms

Local error

Found 4 expressions with local error:

4.7b
(- (* x x) (* (* y 4.0) y))
29.1b
(sqrt (+ (* x x) (* (* y 4.0) y)))
29.1b
(sqrt (+ (* x x) (* (* y 4.0) y)))
30.6b
(/ (- (* x x) (* (* y 4.0) y)) (* (sqrt (+ (* x x) (* (* y 4.0) y))) (sqrt (+ (* x x) (* (* y 4.0) y)))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity flip3-+ associate-/r/ flip-+
6×pow1 sqrt-prod add-log-exp
4×frac-times
3×times-frac associate-/l*
2×cbrt-undiv rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-*r/ div-exp associate-*l/ flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 74
Calls
4 calls:
16.0ms
(- (* x x) (* (* y 4.0) y))
16.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
16.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
90.0ms
(/ (- (* x x) (* (* y 4.0) y)) (* (sqrt (+ (* x x) (* (* y 4.0) y))) (sqrt (+ (* x x) (* (* y 4.0) y)))))

series386.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (* x x) (* (* y 4.0) y))
98.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
104.0ms
(sqrt (+ (* x x) (* (* y 4.0) y)))
102.0ms
(/ (- (* x x) (* (* y 4.0) y)) (* (sqrt (+ (* x x) (* (* y 4.0) y))) (sqrt (+ (* x x) (* (* y 4.0) y)))))

simplify2.5s

Counts
86 → 86
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01082118
12891662
29231450
335861426
done50001426

prune361.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.6b

regimes3.0ms