Details

Time bar (total: 13.7s)

sample70.0ms

Algorithm
intervals
Results
50.0ms274×body80valid

simplify9.0ms

Counts
1 → 1
Iterations
IterNodes
215
115
011

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.3b
(+ (* x.re y.re) (* x.im y.im))
22.8b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
4×flip3-+ flip-+
3×pow1 associate-/r* associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
3 → 53
Calls
3 calls:
6.0ms
(+ (* y.re y.re) (* y.im y.im))
13.0ms
(+ (* x.re y.re) (* x.im y.im))
32.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series196.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(+ (* y.re y.re) (* y.im y.im))
43.0ms
(+ (* x.re y.re) (* x.im y.im))
108.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts
62 → 62
Iterations
IterNodes
34321
21105
1280
098

prune639.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* x.re y.re) (* x.im y.im))
12.8b
(/ (+ (* 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)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log 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 clear-num sum-log frac-2neg div-exp div-inv
Counts
4 → 84
Calls
4 calls:
13.0ms
(+ (* x.re y.re) (* x.im y.im))
53.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
11.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series359.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ (* 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))))
67.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
69.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify949.0ms

Counts
96 → 96
Iterations
IterNodes
32590
2900
1279
0117

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 20.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* x.re y.re) (* x.im y.im))
12.9b
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (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)))

rewrite104.0ms

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 sum-log 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 94
Calls
4 calls:
11.0ms
(+ (* x.re y.re) (* x.im y.im))
63.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
11.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* x.re y.re) (* x.im y.im))
118.0ms
(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.6s

Counts
106 → 106
Iterations
IterNodes
33610
21139
1400
0146

prune1.5s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 20.7b

localize36.0ms

Local error

Found 4 expressions with local error:

12.8b
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.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)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
12×add-sqr-sqrt
10×flip3-+ flip-+
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt sqrt-prod
8×associate-/r/
7×pow1
4×frac-times add-log-exp
3×rem-sqrt-square sqrt-pow1 times-frac pow1/2 associate-/l*
2×cbrt-undiv div-exp associate-*l/ associate-*r/ associate-/l/
1×clear-num associate-/r* frac-2neg prod-exp cbrt-unprod div-inv
Counts
4 → 76
Calls
4 calls:
40.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
5.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series246.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
42.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
48.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify652.0ms

Counts
88 → 88
Iterations
IterNodes
32015
2708
1268
0107

prune1.2s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 20.7b

regimes601.0ms

Accuracy

0% (2.8b remaining)

Error of 25.7b against oracle of 22.9b and baseline of 25.7b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
220
120
015

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.0s8465×body80valid