Details

Time bar (total: 3.5s)

sample21.0ms

Algorithm
intervals
Results
8.0ms267×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0177
1217
2217
done217

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
23.4b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite38.0ms

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 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 47
Calls
2 calls:
7.0ms
(+ (* y.re y.re) (* y.im y.im))
29.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series117.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(+ (* y.re y.re) (* y.im y.im))
88.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify118.0ms

Counts
53 → 53
Iterations

Useful iterations: 3 (114.0ms)

IterNodesCost
0255454
11079405
24324392
35001391
done5001391

prune174.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(hypot y.re y.im)
0.3b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
15.4b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
155×add-exp-log
86×prod-exp
57×div-exp
45×add-cbrt-cube
35×1-exp
16×cbrt-unprod
14×cbrt-undiv
12×add-sqr-sqrt rec-exp
10×add-cube-cbrt *-un-lft-identity
9×times-frac
7×associate-*r* associate-*l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×hypot-udef
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative unswap-sqr
Counts
4 → 122
Calls
4 calls:
0.0ms
(hypot y.re y.im)
0.0ms
(hypot y.re y.im)
47.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
7.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series404.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(hypot y.re y.im)
46.0ms
(hypot y.re y.im)
184.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
125.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify41.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
04791092
11588808
25001806
done5001806

prune257.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(hypot y.re y.im)
0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
15.4b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
23×add-exp-log
18×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
4×pow1 expm1-log1p-u prod-exp associate-/r* log1p-expm1-u div-inv add-log-exp
2×hypot-udef frac-2neg 1-exp clear-num cbrt-unprod
1×associate-/l/
Counts
4 → 99
Calls
4 calls:
0.0ms
(hypot y.re y.im)
0.0ms
(hypot y.re y.im)
12.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series352.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(hypot y.re y.im)
47.0ms
(hypot y.re y.im)
127.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
129.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify74.0ms

Counts
111 → 111
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0301780
11076689
23153689
35001681
done5001681

prune300.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(hypot y.re y.im)
0.1b
(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
15.6b
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
30×add-cbrt-cube
26×prod-exp
23×div-exp
19×add-sqr-sqrt
13×*-un-lft-identity associate-*r*
12×add-cube-cbrt times-frac
9×cbrt-undiv 1-exp cbrt-unprod
6×pow1
4×expm1-log1p-u rec-exp log1p-expm1-u add-log-exp
3×associate-*l* unswap-sqr
2×hypot-udef associate-*r/ un-div-inv div-inv associate-/l/
1×frac-2neg pow-prod-down clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 96
Calls
4 calls:
0.0ms
(hypot y.re y.im)
0.0ms
(hypot y.re y.im)
16.0ms
(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
14.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(hypot y.re y.im)
48.0ms
(hypot y.re y.im)
128.0ms
(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))) (* (hypot y.re y.im) 1))
129.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

simplify44.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389743
11595591
25001562
done5001562

prune224.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.9b

regimes184.0ms

Accuracy

36.3% (7.1b remaining)

Error of 12.5b against oracle of 5.4b and baseline of 16.6b

bsearch54.0ms

Steps
ItersRangePoint
8
6.634311055573296e+114
4.3578969134012087e+117
1.7533497436461888e+117
4
-6.90058054258779e+154
-3.4887686080401957e+154
-5.744231621044319e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
13215
23215
done3215

end0.0ms

sample551.0ms

Algorithm
intervals
Results
273.0ms8463×body80valid