Details

Time bar (total: 17.4s)

sample34.0ms

Algorithm
intervals
Results
22.0ms275×body80valid

simplify47.0ms

Counts
1 → 1
Iterations
IterNodes
680
580
476
356
240
121
011

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.im y.im (* y.re y.re))
0.5b
(- (* x.im y.re) (* x.re y.im))
27.2b
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite44.0ms

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 add-log-exp
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff fma-udef div-inv
Counts
3 → 61
Calls
3 calls:
0.0ms
(fma y.im y.im (* y.re y.re))
15.0ms
(- (* x.im y.re) (* x.re y.im))
27.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series264.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(fma y.im y.im (* y.re y.re))
70.0ms
(- (* x.im y.re) (* x.re y.im))
133.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify1.0s

Counts
70 → 70
Iterations
IterNodes
32977
2789
1234
099

prune918.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 26.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
14.4b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
31.8b
(sqrt (fma y.im y.im (* y.re y.re)))
31.8b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite44.0ms

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 add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 fma-udef hypot-def flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
4 → 96
Calls
4 calls:
8.0ms
(- (* x.im y.re) (* x.re y.im))
30.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* x.im y.re) (* x.re y.im))
164.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
48.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
53.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify723.0ms

Counts
108 → 108
Iterations
IterNodes
32058
2728
1269
0117

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
0.5b
(- (* x.im y.re) (* x.re y.im))
14.4b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
31.8b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
91×add-sqr-sqrt
90×*-un-lft-identity add-cube-cbrt
45×sqrt-prod
16×associate-/l*
11×add-cbrt-cube add-exp-log
9×associate-/r* div-inv
6×add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×div-sub associate-/l/
2×clear-num frac-2neg flip3-- flip--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff fma-udef hypot-def
Counts
4 → 183
Calls
4 calls:
36.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
14.0ms
(- (* x.im y.re) (* x.re y.im))
18.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series564.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
64.0ms
(- (* x.im y.re) (* x.re y.im))
188.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
77.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.3s

Counts
195 → 195
Iterations
IterNodes
35275
21592
1589
0258

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.im y.re)
0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b
(- (* x.im y.re) (* x.re y.im))
14.4b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

rewrite76.0ms

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 add-log-exp
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×div-sub associate-/l/
2×clear-num frac-2neg flip3-- flip--
1×hypot-udef sub-neg fma-neg diff-log prod-diff
Counts
4 → 135
Calls
4 calls:
0.0ms
(hypot y.im y.re)
18.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
17.0ms
(- (* x.im y.re) (* x.re y.im))
39.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

series474.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(hypot y.im y.re)
182.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
71.0ms
(- (* x.im y.re) (* x.re y.im))
135.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

simplify2.8s

Counts
147 → 147
Iterations
IterNodes
35219
21449
1466
0198

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

regimes243.0ms

Accuracy

32.4% (7.2b remaining)

Error of 12.8b against oracle of 5.5b and baseline of 16.2b

bsearch89.0ms

Steps
ItersRangePoint
7
8.240977246969897e+91
1.9142861966646984e+93
1.8584161242035747e+93
7
-1.542727211461463e+154
-3.8584650617426363e+152
-1.4037038847053747e+154

simplify6.0ms

Iterations
IterNodes
224
124
021

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.2s8499×body80valid