Details

Time bar (total: 35.3s)

sample426.0ms

Algorithm
intervals
Results
137.0ms80×body1280valid
100.0ms254×body80valid
47.0ms48×body640valid
9.0ms15×body320valid
5.0ms9×body160valid

simplify3.5s

Counts
1 → 1
Iterations
IterNodes
65780
5821
4208
395
262
135
019

prune46.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
1.5b
(* (atan2 x.im x.re) y.re)
2.3b
(* (atan2 x.im x.re) y.im)
34.3b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×pow1
10×add-cbrt-cube associate-*r* add-exp-log
9×associate-*l*
6×log-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum log-pow fma-udef
Counts
4 → 81
Calls
4 calls:
15.0ms
(* y.re (log (hypot x.re x.im)))
23.0ms
(* (atan2 x.im x.re) y.re)
11.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* y.re (log (hypot x.re x.im)))
31.0ms
(* (atan2 x.im x.re) y.re)
33.0ms
(* (atan2 x.im x.re) y.im)
192.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
93 → 93
Iterations
IterNodes
42764
31331
2624
1284
0150

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.6b

localize80.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.im)
1.5b
(* (atan2 x.im x.re) y.re)
2.4b
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
34.3b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt pow1 add-exp-log
9×add-cbrt-cube
8×*-un-lft-identity add-cube-cbrt
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
2×*-commutative unswap-sqr
1×cos-sum pow1/3 fma-udef
Counts
4 → 68
Calls
4 calls:
1.0ms
(cbrt y.im)
6.0ms
(* (atan2 x.im x.re) y.re)
38.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series514.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(cbrt y.im)
28.0ms
(* (atan2 x.im x.re) y.re)
110.0ms
(* (atan2 x.im x.re) (* (cbrt y.im) (cbrt y.im)))
153.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify4.3s

Counts
80 → 80
Iterations
IterNodes
46219
31844
2706
1286
0133

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.6b

localize70.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (atan2 x.im x.re) y.re)
2.3b
(* (atan2 x.im x.re) y.im)
23.1b
(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
34.3b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×cos-sum fma-udef remove-posit16
Counts
4 → 64
Calls
4 calls:
6.0ms
(* (atan2 x.im x.re) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
0.0ms
(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
3.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (atan2 x.im x.re) y.re)
36.0ms
(* (atan2 x.im x.re) y.im)
150.0ms
(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
143.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify2.0s

Counts
76 → 76
Iterations
IterNodes
42614
31190
2495
1218
0116

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize114.0ms

Local error

Found 4 expressions with local error:

23.1b
(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
34.3b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.3b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
34.3b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
3×cos-sum fma-udef
1×remove-posit16
Counts
4 → 44
Calls
4 calls:
1.0ms
(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series680.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
157.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
167.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))
200.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.6s

Counts
56 → 56
Iterations
IterNodes
53087
41161
3431
2201
1108
062

prune2.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

regimes703.0ms

Accuracy

0% (0.7b remaining)

Error of 4.2b against oracle of 3.5b and baseline of 4.2b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
225
125
020

end0.0ms

sample11.0s

Algorithm
intervals
Results
4.2s2042×body1280valid
3.5s7968×body80valid
2.0s1466×body640valid
547.0ms627×body320valid
223.0ms296×body160valid