Details

Time bar (total: 11.2s)

sample34.0ms

Algorithm
intervals
Results
16.0ms271×body80valid

simplify50.0ms

Counts
1 → 1
Iterations
IterNodes
done94
694
590
476
356
240
121
011

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.im y.im (* y.re y.re))
0.3b
(fma (- y.im) x.re (* x.im y.re))
25.3b
(/ (fma (- y.im) x.re (* x.im y.re)) (fma y.im y.im (* y.re y.re)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
3 → 49
Calls
3 calls:
0.0ms
(fma y.im y.im (* y.re y.re))
0.0ms
(fma (- y.im) x.re (* x.im y.re))
4.0ms
(/ (fma (- y.im) x.re (* x.im y.re)) (fma y.im y.im (* y.re y.re)))

series213.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(fma y.im y.im (* y.re y.re))
66.0ms
(fma (- y.im) x.re (* x.im y.re))
101.0ms
(/ (fma (- y.im) x.re (* x.im y.re)) (fma y.im y.im (* y.re y.re)))

simplify719.0ms

Counts
58 → 58
Iterations
IterNodes
done5001
31516
2344
1118
074

prune391.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot y.im y.re))
0.2b
(* (/ 1 (hypot y.im y.re)) (/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.im y.re)))
0.3b
(fma x.re (- y.im) (* y.re x.im))
16.4b
(/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.im y.re))

rewrite53.0ms

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 pow-prod-down associate-*l/ associate-*r/ *-commutative fma-udef pow-flip inv-pow
Counts
4 → 130
Calls
4 calls:
6.0ms
(/ 1 (hypot y.im y.re))
32.0ms
(* (/ 1 (hypot y.im y.re)) (/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.im y.re)))
0.0ms
(fma x.re (- y.im) (* y.re x.im))
8.0ms
(/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.im y.re))

series616.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ 1 (hypot y.im y.re))
265.0ms
(* (/ 1 (hypot y.im y.re)) (/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.im y.re)))
72.0ms
(fma x.re (- y.im) (* y.re x.im))
211.0ms
(/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.im y.re))

simplify1.8s

Counts
142 → 142
Iterations
IterNodes
done5000
22778
1407
0154

prune709.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.im y.re)
0.1b
(/ (/ (fma y.im (- x.re) (* y.re x.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.3b
(fma y.im (- x.re) (* y.re x.im))
16.4b
(/ (fma y.im (- x.re) (* y.re x.im)) (hypot y.im y.re))

rewrite18.0ms

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×clear-num frac-2neg
1×hypot-udef fma-udef associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot y.im y.re)
9.0ms
(/ (/ (fma y.im (- x.re) (* y.re x.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.0ms
(fma y.im (- x.re) (* y.re x.im))
4.0ms
(/ (fma y.im (- x.re) (* y.re x.im)) (hypot y.im y.re))

series397.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(hypot y.im y.re)
144.0ms
(/ (/ (fma y.im (- x.re) (* y.re x.im)) (hypot y.im y.re)) (hypot y.im y.re))
58.0ms
(fma y.im (- x.re) (* y.re x.im))
143.0ms
(/ (fma y.im (- x.re) (* y.re x.im)) (hypot y.im y.re))

simplify749.0ms

Counts
133 → 133
Iterations
IterNodes
done5000
21526
1352
0168

prune996.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot y.im y.re) (fma y.im (- x.re) (* y.re x.im))))
0.2b
(* (/ 1 (hypot y.im y.re)) (/ 1 (/ (hypot y.im y.re) (fma y.im (- x.re) (* y.re x.im)))))
0.3b
(fma y.im (- x.re) (* y.re x.im))
16.4b
(/ (hypot y.im y.re) (fma y.im (- x.re) (* y.re x.im)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
187×times-frac
143×add-sqr-sqrt
107×*-un-lft-identity
100×add-exp-log
96×add-cube-cbrt
50×div-exp
44×associate-*r*
32×add-cbrt-cube
28×prod-exp
17×rec-exp 1-exp
16×associate-/r*
15×unswap-sqr
13×cbrt-undiv associate-*l*
11×div-inv
9×pow1
6×cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down pow-flip inv-pow
2×clear-num frac-2neg associate-/r/
1×frac-times associate-*l/ associate-*r/ un-div-inv *-commutative fma-udef
Counts
4 → 240
Calls
4 calls:
13.0ms
(/ 1 (/ (hypot y.im y.re) (fma y.im (- x.re) (* y.re x.im))))
67.0ms
(* (/ 1 (hypot y.im y.re)) (/ 1 (/ (hypot y.im y.re) (fma y.im (- x.re) (* y.re x.im)))))
0.0ms
(fma y.im (- x.re) (* y.re x.im))
6.0ms
(/ (hypot y.im y.re) (fma y.im (- x.re) (* y.re x.im)))

series573.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ 1 (/ (hypot y.im y.re) (fma y.im (- x.re) (* y.re x.im))))
213.0ms
(* (/ 1 (hypot y.im y.re)) (/ 1 (/ (hypot y.im y.re) (fma y.im (- x.re) (* y.re x.im)))))
51.0ms
(fma y.im (- x.re) (* y.re x.im))
128.0ms
(/ (hypot y.im y.re) (fma y.im (- x.re) (* y.re x.im)))

simplify458.0ms

Counts
252 → 252
Iterations
IterNodes
done5001
1955
0292

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.3b

regimes512.0ms

Accuracy

32.6% (7.4b remaining)

Error of 13.1b against oracle of 5.7b and baseline of 16.7b

bsearch95.0ms

Steps
ItersRangePoint
8
8.82264561323041e+113
2.2603517154234716e+117
1.0192818396927862e+117
9
-1.1149747458205285e+104
-2.605970981926323e+98
-9.323590362566379e+102

simplify11.0ms

Iterations
IterNodes
done40
340
238
129
022

end0.0ms

sample1.2s

Algorithm
intervals
Results
736.0ms8499×body80valid