Details

Time bar (total: 11.8s)

sample48.0ms

Algorithm
intervals
Results
27.0ms270×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11515
done1515

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(+ (* x.re y.re) (* x.im y.im))
24.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite69.0ms

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
4×flip3-+ flip-+
3×pow1 associate-/r* associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 53
Calls
3 calls:
11.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(+ (* x.re y.re) (* x.im y.im))
47.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series262.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ (* y.re y.re) (* y.im y.im))
66.0ms
(+ (* x.re y.re) (* x.im y.im))
142.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts
62 → 62
Iterations

Useful iterations: 2 (172.0ms)

IterNodesCost
0991090
12701067
2866951
32515951
done5001951

prune263.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
14.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
16.0ms
(+ (* x.re y.re) (* x.im y.im))
57.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ (* x.re y.re) (* x.im y.im))
163.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
45.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts
96 → 96
Iterations

Useful iterations: 3 (610.0ms)

IterNodesCost
01171780
12751649
27751541
320601525
done50001525

prune453.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.9b

localize26.0ms

Local error

Found 4 expressions with local error:

7.7b
(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
27.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
137×add-sqr-sqrt
108×sqrt-prod
99×times-frac
57×*-un-lft-identity
45×add-cube-cbrt
33×associate-*r* associate-*l*
28×unswap-sqr
26×add-exp-log
16×add-cbrt-cube
14×sqrt-div
9×pow1
8×div-exp prod-exp
5×flip3-+ flip-+
4×cbrt-undiv associate-/r/ cbrt-unprod add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×rec-exp 1-exp div-inv
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 163
Calls
4 calls:
157.0ms
(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
11.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
63.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
44.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
63.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts
175 → 175
Iterations

Useful iterations: 2 (492.0ms)

IterNodesCost
01985510
15565091
219724307
done50004307

prune631.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.7b
(+ (* x.re y.re) (* x.im y.im))
24.7b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×add-cube-cbrt times-frac
17×add-exp-log
15×associate-*r*
11×add-cbrt-cube
8×add-log-exp
7×pow1
6×flip3-+ flip-+
4×div-exp prod-exp associate-/r/
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv +-commutative frac-times rec-exp 1-exp associate-*l/ sum-log cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 97
Calls
4 calls:
17.0ms
(+ (* y.re y.re) (* y.im y.im))
29.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
17.0ms
(+ (* x.re y.re) (* x.im y.im))
68.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series279.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (* y.re y.re) (* y.im y.im))
70.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
45.0ms
(+ (* x.re y.re) (* x.im y.im))
129.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify3.1s

Counts
109 → 109
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
01401789
13841627
212681431
342981417
done50001417

prune315.0ms

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 21.9b

regimes8.0ms