Details

Time bar (total: 8.3s)

sample19.0ms

Algorithm
intervals
Results
9.0ms264×body80valid

simplify51.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.re y.re (* y.im y.im))
1.2b
(- (* x.im y.re) (* x.re y.im))
25.0b
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite12.0ms

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))
3.0ms
(- (* x.im y.re) (* x.re y.im))
7.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series159.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(fma y.re y.re (* y.im y.im))
35.0ms
(- (* x.im y.re) (* x.re y.im))
88.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.0s

Counts
67 → 67
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0971039
12261011
2909892
34055892
done5000890

prune190.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.im y.re)
0.2b
(* (/ 1 (hypot y.im y.re)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)))
1.2b
(- (* x.im y.re) (* x.re y.im))
15.9b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
28×add-exp-log *-un-lft-identity
26×add-cube-cbrt
18×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×pow1 add-log-exp unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u
3×associate-/r* div-inv associate-/l*
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg hypot-udef frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 116
Calls
4 calls:
0.0ms
(hypot y.im y.re)
21.0ms
(* (/ 1 (hypot y.im y.re)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)))
3.0ms
(- (* x.im y.re) (* x.re y.im))
7.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

series373.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(hypot y.im y.re)
180.0ms
(* (/ 1 (hypot y.im y.re)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)))
35.0ms
(- (* x.im y.re) (* x.re y.im))
112.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

simplify1.1s

Counts
128 → 128
Iterations

Useful iterations: 2 (173.0ms)

IterNodesCost
01712225
14922088
218901817
done50001817

prune332.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.im y.re)
0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
1.2b
(- (* x.im y.re) (* x.re y.im))
15.9b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 131
Calls
4 calls:
0.0ms
(hypot y.im y.re)
9.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
3.0ms
(- (* x.im y.re) (* x.re y.im))
7.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

series310.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(hypot y.im y.re)
113.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
35.0ms
(- (* x.im y.re) (* x.re y.im))
115.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

simplify733.0ms

Counts
143 → 143
Iterations

Useful iterations: 2 (152.0ms)

IterNodesCost
01942874
14802796
216752600
done50012600

prune385.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x.re (hypot y.im y.re))
0.1b
(/ (- (/ y.re (/ (hypot y.im y.re) x.im)) (* y.im (/ x.re (hypot y.im y.re)))) (hypot y.im y.re))
7.0b
(* y.im (/ x.re (hypot y.im y.re)))
7.8b
(/ y.re (/ (hypot y.im y.re) x.im))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
103×times-frac
75×add-sqr-sqrt
70×add-cube-cbrt *-un-lft-identity
19×associate-/r*
18×add-exp-log add-cbrt-cube
13×associate-*r*
9×associate-/l*
8×div-inv
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*l* clear-num associate-/l/
2×associate-*r/ prod-exp cbrt-unprod unswap-sqr
1×flip3-- div-sub pow-prod-down associate-/r/ *-commutative frac-sub flip--
Counts
4 → 168
Calls
4 calls:
2.0ms
(/ x.re (hypot y.im y.re))
79.0ms
(/ (- (/ y.re (/ (hypot y.im y.re) x.im)) (* y.im (/ x.re (hypot y.im y.re)))) (hypot y.im y.re))
7.0ms
(* y.im (/ x.re (hypot y.im y.re)))
5.0ms
(/ y.re (/ (hypot y.im y.re) x.im))

series524.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ x.re (hypot y.im y.re))
297.0ms
(/ (- (/ y.re (/ (hypot y.im y.re) x.im)) (* y.im (/ x.re (hypot y.im y.re)))) (hypot y.im y.re))
77.0ms
(* y.im (/ x.re (hypot y.im y.re)))
93.0ms
(/ y.re (/ (hypot y.im y.re) x.im))

simplify830.0ms

Counts
180 → 180
Iterations

Useful iterations: 2 (213.0ms)

IterNodesCost
02772728
16182617
224912419
done50012419

prune511.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes138.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01423
12019
22419
done2419

end0.0ms

sample510.0ms

Algorithm
intervals
Results
296.0ms8495×body80valid