Details

Time bar (total: 15.0s)

sample36.0ms

Algorithm
intervals
Results
21.0ms268×body80valid

simplify96.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.re y.re (* y.im y.im))
1.4b
(- (* x.im y.re) (* x.re y.im))
24.9b
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-exp-log add-cbrt-cube add-log-exp
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num fma-udef div-inv
Counts
3 → 58
Calls
3 calls:
1.0ms
(fma y.re y.re (* y.im y.im))
17.0ms
(- (* x.im y.re) (* x.re y.im))
41.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series235.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(fma y.re y.re (* y.im y.im))
55.0ms
(- (* x.im y.re) (* x.re y.im))
136.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.9s

Counts
67 → 67
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0971039
12281011
2761906
32655892
done5000886

prune270.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
1.4b
(- (* x.im y.re) (* x.re y.im))
15.6b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
34×times-frac
27×add-exp-log *-un-lft-identity
25×add-cube-cbrt
17×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×unswap-sqr
5×pow1 cbrt-undiv add-log-exp
4×cbrt-unprod
3×expm1-log1p-u associate-/r* log1p-expm1-u div-inv associate-/l*
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 106
Calls
3 calls:
60.0ms
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
13.0ms
(- (* x.im y.re) (* x.re y.im))
29.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series508.0ms

Counts
3 → 9
Calls
3 calls:
264.0ms
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
66.0ms
(- (* x.im y.re) (* x.re y.im))
177.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify2.3s

Counts
115 → 115
Iterations

Useful iterations: 2 (263.0ms)

IterNodesCost
01642165
14472018
215051765
done50001765

prune351.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
1.4b
(- (* x.im y.re) (* x.re y.im))
15.6b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 121
Calls
3 calls:
30.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
15.0ms
(- (* x.im y.re) (* x.re y.im))
20.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series355.0ms

Counts
3 → 9
Calls
3 calls:
151.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
46.0ms
(- (* x.im y.re) (* x.re y.im))
158.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify2.3s

Counts
130 → 130
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01872814
14452738
212442548
344722493
done50002490

prune659.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im))
0.1b
(/ (- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im)) (hypot y.re y.im))
1.0b
(* (/ y.re (hypot y.re y.im)) x.im)
9.4b
(* (/ x.re (hypot y.re y.im)) y.im)

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
29×times-frac
28×add-cube-cbrt *-un-lft-identity
26×associate-*l*
16×add-exp-log add-cbrt-cube
10×associate-*l/
8×pow1
6×associate-*r* add-log-exp
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u associate-/l/ unswap-sqr
3×cbrt-undiv div-exp associate-/r* div-inv associate-/l*
2×flip3-- pow-prod-down *-commutative frac-sub flip-- sub-div
1×sub-neg frac-2neg fma-neg diff-log div-sub prod-diff clear-num
Counts
4 → 120
Calls
4 calls:
24.0ms
(- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im))
38.0ms
(/ (- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im)) (hypot y.re y.im))
26.0ms
(* (/ y.re (hypot y.re y.im)) x.im)
16.0ms
(* (/ x.re (hypot y.re y.im)) y.im)

series942.0ms

Counts
4 → 12
Calls
4 calls:
255.0ms
(- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im))
447.0ms
(/ (- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im)) (hypot y.re y.im))
135.0ms
(* (/ y.re (hypot y.re y.im)) x.im)
105.0ms
(* (/ x.re (hypot y.re y.im)) y.im)

simplify1.5s

Counts
132 → 132
Iterations

Useful iterations: 2 (367.0ms)

IterNodesCost
02032079
14831982
214621825
done50001825

prune682.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes163.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: done (4.0ms)

IterNodesCost
01627
12121
done2119

end0.0ms

sample1.3s

Algorithm
intervals
Results
881.0ms8530×body80valid