Details

Time bar (total: 18.4s)

sample38.0ms

Algorithm
intervals
Results
21.0ms272×body80valid

simplify79.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.re y.re (* y.im y.im))
0.7b
(- (* x.im y.re) (* x.re y.im))
27.2b
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite35.0ms

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:
0.0ms
(fma y.re y.re (* y.im y.im))
9.0ms
(- (* x.im y.re) (* x.re y.im))
24.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series252.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(fma y.re y.re (* y.im y.im))
63.0ms
(- (* x.im y.re) (* x.re y.im))
132.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify3.1s

Counts
67 → 67
Iterations

Useful iterations: done (3.1s)

IterNodesCost
0971039
12281011
2761906
32655892
done5000886

prune363.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.0b

localize17.0ms

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)))
0.7b
(- (* x.im y.re) (* x.re y.im))
16.6b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite86.0ms

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:
35.0ms
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
24.0ms
(- (* x.im y.re) (* x.re y.im))
21.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series557.0ms

Counts
3 → 9
Calls
3 calls:
288.0ms
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
70.0ms
(- (* x.im y.re) (* x.re y.im))
198.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify2.2s

Counts
115 → 115
Iterations

Useful iterations: 2 (285.0ms)

IterNodesCost
01642165
14472018
215051765
done50001765

prune502.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.7b
(- (* x.im y.re) (* x.re y.im))
16.6b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite90.0ms

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:
36.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
9.0ms
(- (* x.im y.re) (* x.re y.im))
37.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series467.0ms

Counts
3 → 9
Calls
3 calls:
207.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
65.0ms
(- (* x.im y.re) (* x.re y.im))
195.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify3.4s

Counts
130 → 130
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01872814
14452738
212442548
344722493
done50002490

prune559.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y.re (hypot y.re y.im))
0.0b
(/ (- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im)) (hypot y.re y.im))
3.7b
(* (/ y.re (hypot y.re y.im)) x.im)
7.2b
(* (/ x.re (hypot y.re y.im)) y.im)

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
38×times-frac
36×add-cube-cbrt *-un-lft-identity
26×associate-*l*
18×add-exp-log add-cbrt-cube
8×pow1
6×associate-*r* associate-*l/ associate-/r* associate-/l*
4×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv associate-/l/ add-log-exp unswap-sqr
2×frac-2neg pow-prod-down clear-num *-commutative
1×flip3-- div-sub frac-sub flip-- sub-div
Counts
4 → 131
Calls
4 calls:
5.0ms
(/ y.re (hypot y.re y.im))
57.0ms
(/ (- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im)) (hypot y.re y.im))
25.0ms
(* (/ y.re (hypot y.re y.im)) x.im)
15.0ms
(* (/ x.re (hypot y.re y.im)) y.im)

series859.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ y.re (hypot y.re y.im))
493.0ms
(/ (- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im)) (hypot y.re y.im))
147.0ms
(* (/ y.re (hypot y.re y.im)) x.im)
117.0ms
(* (/ x.re (hypot y.re y.im)) y.im)

simplify3.6s

Counts
143 → 143
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01971952
14471883
213671723
346461723
done50001722

prune530.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes171.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
11319
done1319

end0.0ms

sample1.3s

Algorithm
intervals
Results
881.0ms8480×body80valid