Details

Time bar (total: 27.1s)

sample45.0ms

Algorithm
intervals
Results
21.0ms263×body80valid

simplify19.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize38.0ms

Local error

Found 2 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
25.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite107.0ms

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:
18.0ms
(+ (* x.re y.re) (* x.im y.im))
86.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series261.0ms

Counts
2 → 6
Calls
2 calls:
82.0ms
(+ (* x.re y.re) (* x.im y.im))
179.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify3.7s

Counts
53 → 53
Iterations
IterNodes
done5005
32703
2858
1247
090

prune589.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.8b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (* x.re y.re) (* x.im y.im))
16.1b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite134.0ms

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-+
4×expm1-log1p-u log1p-expm1-u
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ hypot-def associate-/l/
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 95
Calls
4 calls:
17.0ms
(+ (* x.re y.re) (* x.im y.im))
68.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
17.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(+ (* x.re y.re) (* x.im y.im))
226.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
71.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
77.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.4s

Counts
107 → 107
Iterations
IterNodes
done5001
32590
2906
1298
0123

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.4b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))
0.5b
(+ (* x.re y.re) (* x.im y.im))
16.1b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
98×add-sqr-sqrt
97×add-cube-cbrt *-un-lft-identity
51×sqrt-prod
27×associate-/l*
12×sqrt-div
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
8×flip3-+ flip-+
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg clear-num
1×+-commutative rem-sqrt-square fma-def sqrt-pow1 pow1/2 sum-log hypot-def
Counts
4 → 193
Calls
4 calls:
97.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))
23.0ms
(+ (* x.re y.re) (* x.im y.im))
74.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
18.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series711.0ms

Counts
4 → 12
Calls
4 calls:
334.0ms
(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (hypot y.re y.im))
67.0ms
(+ (* x.re y.re) (* x.im y.im))
237.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
74.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.7s

Counts
205 → 205
Iterations
IterNodes
done5000
34798
21560
1722
0276

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot y.re y.im))
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im)))
0.5b
(fma y.im x.im (* y.re x.re))
16.1b
(/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp
2×frac-2neg clear-num
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef inv-pow
Counts
4 → 130
Calls
4 calls:
11.0ms
(/ 1 (hypot y.re y.im))
60.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im)))
1.0ms
(fma y.im x.im (* y.re x.re))
27.0ms
(/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im))

series765.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ 1 (hypot y.re y.im))
327.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im)))
90.0ms
(fma y.im x.im (* y.re x.re))
229.0ms
(/ (fma y.im x.im (* y.re x.re)) (hypot y.re y.im))

simplify3.4s

Counts
142 → 142
Iterations
IterNodes
done5001
21269
1387
0152

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

regimes759.0ms

Accuracy

27% (10.7b remaining)

Error of 12.9b against oracle of 2.2b and baseline of 16.8b

bsearch122.0ms

Steps
ItersRangePoint
5
5.89260587928172e+117
1.3020347336788914e+118
7.0425014975515e+117
8
-3.274521271539268e+173
-8.64964935901111e+169
-9.070380995118473e+169

simplify9.0ms

Iterations
IterNodes
done35
335
231
127
020

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.5s8479×body80valid