Details

Time bar (total: 22.9s)

sample309.0ms

Algorithm
intervals
Results
59.0ms61×body1280valid
32.0ms248×body80valid
25.0ms42×body640valid
9.0ms21×body320valid
2.0ms8×body160valid

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
019784
135654
263654
399654
4249654
51130654
done5001654

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
0.9b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
32.9b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite43.0ms

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 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow fma-udef
Counts
4 → 77
Calls
4 calls:
13.0ms
(* y.re (log (hypot x.re x.im)))
15.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* y.re (log (hypot x.re x.im)))
22.0ms
(* (atan2 x.im x.re) y.re)
28.0ms
(* (atan2 x.im x.re) y.im)
263.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.2s

Counts
89 → 89
Iterations

Useful iterations: done (1.1s)

IterNodesCost
013825555
127025013
287124931
done500124586

prune888.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
0.9b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
32.9b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow fma-udef
Counts
4 → 77
Calls
4 calls:
7.0ms
(* y.re (log (hypot x.re x.im)))
5.0ms
(* (atan2 x.im x.re) y.re)
5.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* y.re (log (hypot x.re x.im)))
18.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
195.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.0s

Counts
89 → 89
Iterations

Useful iterations: done (1.0s)

IterNodesCost
013825555
127025013
287124931
done500124586

prune928.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (log (hypot x.re x.im)))
0.9b
(* (atan2 x.im x.re) y.re)
1.7b
(* (atan2 x.im x.re) y.im)
32.9b
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

rewrite33.0ms

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 log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sin-sum log-pow fma-udef
Counts
4 → 77
Calls
4 calls:
13.0ms
(* y.re (log (hypot x.re x.im)))
10.0ms
(* (atan2 x.im x.re) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(* y.re (log (hypot x.re x.im)))
28.0ms
(* (atan2 x.im x.re) y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
242.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (atan2 x.im x.re) y.re)))

simplify1.1s

Counts
89 → 89
Iterations

Useful iterations: done (1.0s)

IterNodesCost
013825555
127025013
287124931
done500124586

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize106.0ms

Local error

Found 4 expressions with local error:

7.8b
(cbrt (* (atan2 x.im x.re) y.re))
7.8b
(cbrt (* (atan2 x.im x.re) y.re))
7.8b
(cbrt (* (atan2 x.im x.re) y.re))
32.8b
(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

rewrite11.0ms

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 log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×sin-sum fma-udef
Counts
4 → 43
Calls
4 calls:
3.0ms
(cbrt (* (atan2 x.im x.re) y.re))
3.0ms
(cbrt (* (atan2 x.im x.re) y.re))
3.0ms
(cbrt (* (atan2 x.im x.re) y.re))
2.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

series943.0ms

Counts
4 → 12
Calls
4 calls:
508.0ms
(cbrt (* (atan2 x.im x.re) y.re))
80.0ms
(cbrt (* (atan2 x.im x.re) y.re))
90.0ms
(cbrt (* (atan2 x.im x.re) y.re))
264.0ms
(sin (fma (log (hypot x.re x.im)) y.im (* (* (cbrt (* (atan2 x.im x.re) y.re)) (cbrt (* (atan2 x.im x.re) y.re))) (cbrt (* (atan2 x.im x.re) y.re)))))

simplify1.6s

Counts
55 → 55
Iterations

Useful iterations: done (1.6s)

IterNodesCost
07122960
111922931
220722811
348920506
4174218967
done500018850

prune683.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

regimes677.0ms

Accuracy

0% (0.2b remaining)

Error of 3.5b against oracle of 3.3b and baseline of 3.5b

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
0221134
1271134
done271134

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.3s2261×body1280valid
1.7s8009×body80valid
1.1s1409×body640valid
339.0ms558×body320valid
132.0ms54×body2560valid
80.0ms244×body160valid