Details

Time bar (total: 24.4s)

sample361.0ms

Algorithm
intervals
Results
93.0ms256×body80valid
84.0ms68×body1280valid
48.0ms16×body320valid
38.0ms42×body640valid
6.0ms8×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done2030
62030
5823
4210
395
262
135
019

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b
(* y.re (log (hypot x.re x.im)))
2.1b
(* (atan2 x.im x.re) y.re)
2.7b
(* (atan2 x.im x.re) y.im)
34.5b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite45.0ms

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:
14.0ms
(* y.re (log (hypot x.re x.im)))
11.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(* (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)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(* y.re (log (hypot x.re x.im)))
30.0ms
(* (atan2 x.im x.re) y.re)
23.0ms
(* (atan2 x.im x.re) y.im)
175.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify829.0ms

Counts
93 → 93
Iterations
IterNodes
done2002
32002
2736
1298
0150

prune846.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.4b

localize86.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
2.1b
(* (atan2 x.im x.re) y.re)
2.7b
(* (atan2 x.im x.re) y.im)
34.5b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×cbrt-prod
21×pow1
18×*-un-lft-identity
16×add-cube-cbrt
13×associate-*r* associate-*l*
10×add-exp-log
9×swap-sqr
8×add-cbrt-cube
6×pow1/3 log-pow unswap-sqr
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×prod-exp *-commutative cbrt-unprod
2×pow-sqr pow-prod-up
1×pow2 cos-sum pow-plus fma-udef
Counts
4 → 101
Calls
4 calls:
9.0ms
(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
6.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series433.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
31.0ms
(* (atan2 x.im x.re) y.re)
32.0ms
(* (atan2 x.im x.re) y.im)
163.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
113 → 113
Iterations
IterNodes
done2000
42000
31821
2715
1318
0152

prune962.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.4b

localize79.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
2.1b
(* (atan2 x.im x.re) y.re)
2.7b
(* (atan2 x.im x.re) y.im)
34.5b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×cbrt-prod
21×pow1
18×*-un-lft-identity
16×add-cube-cbrt
13×associate-*r* associate-*l*
10×add-exp-log
9×swap-sqr
8×add-cbrt-cube
6×pow1/3 log-pow unswap-sqr
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×prod-exp *-commutative cbrt-unprod
2×pow-sqr pow-prod-up
1×pow2 cos-sum pow-plus fma-udef
Counts
4 → 101
Calls
4 calls:
9.0ms
(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
6.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(* (cbrt (log (hypot x.re x.im))) (cbrt (log (hypot x.re x.im))))
23.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
202.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
113 → 113
Iterations
IterNodes
done2000
42000
31821
2715
1318
0152

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.4b

localize81.0ms

Local error

Found 4 expressions with local error:

2.1b
(* (atan2 x.im x.re) y.re)
2.7b
(* (atan2 x.im x.re) y.im)
23.7b
(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
34.5b
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

rewrite37.0ms

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:
19.0ms
(* (atan2 x.im x.re) y.re)
12.0ms
(* (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)))))
5.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.re)
22.0ms
(* (atan2 x.im x.re) y.im)
173.0ms
(posit16->real (real->posit16 (cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))))
173.0ms
(cos (fma y.im (log (hypot x.re x.im)) (* (atan2 x.im x.re) y.re)))

simplify1.4s

Counts
76 → 76
Iterations
IterNodes
done2010
42010
31445
2495
1219
0116

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.3b

regimes570.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done23
123
019

end0.0ms

sample11.2s

Algorithm
intervals
Results
3.9s1975×body1280valid
3.0s7979×body80valid
2.5s1448×body640valid
1.1s639×body320valid
246.0ms307×body160valid