Details

Time bar (total: 11.7s)

sample35.0ms

Algorithm
intervals
Results
15.0ms265×body80valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x.re y.re) (* x.im y.im))
24.1b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* flip3-+ flip-+ associate-/l*
2×expm1-log1p-u pow1 associate-/r/ log1p-expm1-u associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log fma-def frac-2neg div-exp div-inv
Counts
2 → 47
Calls
2 calls:
12.0ms
(+ (* x.re y.re) (* x.im y.im))
50.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series176.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(+ (* x.re y.re) (* x.im y.im))
137.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify932.0ms

Counts
53 → 53
Iterations
IterNodes
done5000
21059
1248
090

prune315.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(/ 1 (hypot y.re y.im))
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
15.4b
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

rewrite33.0ms

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×clear-num frac-2neg
1×frac-times hypot-udef pow-prod-down associate-*l/ associate-*r/ *-commutative pow-flip inv-pow
Counts
4 → 130
Calls
4 calls:
0.0ms
(hypot y.re y.im)
5.0ms
(/ 1 (hypot y.re y.im))
21.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
4.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series619.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(hypot y.re y.im)
99.0ms
(/ 1 (hypot y.re y.im))
295.0ms
(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
138.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify1.5s

Counts
142 → 142
Iterations
IterNodes
done5000
22850
1407
0154

prune829.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×hypot-udef clear-num frac-2neg
1×associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot y.re y.im)
0.0ms
(hypot y.re y.im)
18.0ms
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series460.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(hypot y.re y.im)
69.0ms
(hypot y.re y.im)
138.0ms
(/ (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
167.0ms
(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify860.0ms

Counts
133 → 133
Iterations
IterNodes
done5000
21628
1355
0161

prune932.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize36.0ms

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.re x.re (* x.im y.im))))
0.2b
(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))))
15.4b
(/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
196×times-frac
151×add-sqr-sqrt
115×*-un-lft-identity
104×add-exp-log add-cube-cbrt
52×div-exp
44×associate-*r*
34×add-cbrt-cube
28×prod-exp
19×associate-/r*
18×rec-exp 1-exp
15×unswap-sqr
14×cbrt-undiv
13×associate-*l*
12×div-inv
10×pow1
9×associate-/l*
6×cbrt-unprod
4×expm1-log1p-u log1p-expm1-u pow-flip inv-pow add-log-exp
3×clear-num frac-2neg pow-prod-down
2×associate-/r/
1×frac-times associate-*l/ associate-*r/ un-div-inv *-commutative
Counts
4 → 263
Calls
4 calls:
7.0ms
(/ 1 (hypot y.re y.im))
21.0ms
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im))))
42.0ms
(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))))
8.0ms
(/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))

series742.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ 1 (hypot y.re y.im))
217.0ms
(/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im))))
300.0ms
(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))))
144.0ms
(/ (hypot y.re y.im) (fma y.re x.re (* x.im y.im)))

simplify627.0ms

Counts
275 → 275
Iterations
IterNodes
done5001
1964
0295

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.6b

regimes508.0ms

Accuracy

25.2% (7.8b remaining)

Error of 14.0b against oracle of 6.2b and baseline of 16.7b

bsearch242.0ms

Steps
ItersRangePoint
8
1.8883840965187804e+99
7.38173445747568e+101
7.287774565713375e+101
7
-1.0095027531688244e+104
-1.7547760984372204e+102
-9.931482377190183e+103
9
-5.173593764286187e+189
-1.1912223558888474e+184
-1.9720499552888294e+188
10
-9.616245507858335e+264
-1.2168755257065468e+252
-1.2360569206326496e+252

simplify4.0ms

Iterations
IterNodes
done34
134
029

end0.0ms

sample1.3s

Algorithm
intervals
Results
777.0ms8448×body80valid