Details

Time bar (total: 14.7s)

sample55.0ms

Algorithm
intervals
Results
27.0ms276×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11515
done1515

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize25.0ms

Local error

Found 2 expressions with local error:

0.6b
(+ (* x.re y.re) (* x.im y.im))
28.7b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 42
Calls
2 calls:
17.0ms
(+ (* x.re y.re) (* x.im y.im))
82.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series186.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(+ (* x.re y.re) (* x.im y.im))
136.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.8s

Counts
48 → 48
Iterations

Useful iterations: 3 (764.0ms)

IterNodesCost
086924
1232906
2767824
32337820
done5000820

prune160.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 28.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* x.re y.re) (* x.im y.im))
18.4b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite87.0ms

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:
8.0ms
(+ (* x.re y.re) (* x.im y.im))
46.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
19.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (* x.re y.re) (* x.im y.im))
123.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms
(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 (454.0ms)

IterNodesCost
01171780
12751649
27751541
320601525
done50001525

prune441.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 25.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* x.re y.re) (* x.im y.im))
18.4b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite76.0ms

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 add-cbrt-cube associate-/l* add-log-exp
5×flip3-+ flip-+
3×associate-/r*
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:
12.0ms
(+ (* x.re y.re) (* x.im y.im))
35.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(+ (* x.re y.re) (* x.im y.im))
94.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
44.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
57.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.3s

Counts
96 → 96
Iterations

Useful iterations: 3 (524.0ms)

IterNodesCost
01151774
12651656
27231554
317421540
445981540
done50011540

prune450.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 25.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* x.re y.re) (* x.im y.im))
18.5b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×flip3-+ sqrt-div flip-+ add-log-exp
5×unswap-sqr
4×prod-exp
3×associate-*l*
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rec-exp 1-exp associate-*r/ pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
4 → 94
Calls
4 calls:
16.0ms
(+ (* x.re y.re) (* x.im y.im))
102.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
14.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(+ (* x.re y.re) (* x.im y.im))
182.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
44.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
46.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.4s

Counts
106 → 106
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
01461886
13781642
211541474
337511458
done50011458

prune386.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 25.7b

regimes396.0ms

Accuracy

17.5% (2.7b remaining)

Error of 25.8b against oracle of 23.1b and baseline of 26.3b

bsearch3.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02156
12956
done2956

end0.0ms

sample1.1s

Algorithm
intervals
Results
615.0ms8489×body80valid