Details

Time bar (total: 7.5s)

sample22.0ms

Algorithm
intervals
Results
11.0ms277×body80valid

simplify47.0ms

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: 27.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.re y.re (* y.im y.im))
0.8b
(- (* x.im y.re) (* x.re y.im))
26.6b
(/ (- (* 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)))

series158.0ms

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))
87.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify1.8s

Counts
67 → 67
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0971039
12261011
2909892
34055892
done5000890

prune193.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (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)))
0.8b
(- (* x.im y.re) (* x.re y.im))
15.5b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv
3×rec-exp 1-exp
2×flip3-- frac-2neg clear-num flip-- associate-/l/
1×frac-times sub-neg pow-flip fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 139
Calls
4 calls:
2.0ms
(/ 1 (hypot y.im y.re))
19.0ms
(* (/ 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))

series389.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ 1 (hypot y.im y.re))
178.0ms
(* (/ 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))
111.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

simplify967.0ms

Counts
151 → 151
Iterations

Useful iterations: 2 (171.0ms)

IterNodesCost
01782462
15092286
220351997
done50001997

prune360.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.8b
(- (* x.im y.re) (* x.re y.im))
15.5b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

rewrite24.0ms

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:
10.0ms
(/ (/ (- (* 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))
8.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

series267.0ms

Counts
3 → 9
Calls
3 calls:
114.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
39.0ms
(- (* x.im y.re) (* x.re y.im))
113.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

simplify874.0ms

Counts
130 → 130
Iterations

Useful iterations: 2 (139.0ms)

IterNodesCost
01872814
14712738
216642548
done50002548

prune331.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ y.im (hypot y.im y.re))
0.1b
(/ (- (/ (* x.im y.re) (hypot y.im y.re)) (* (/ y.im (hypot y.im y.re)) x.re)) (hypot y.im y.re))
1.9b
(* (/ y.im (hypot y.im y.re)) x.re)
9.6b
(/ (* x.im y.re) (hypot y.im y.re))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
31×times-frac
30×add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube
13×associate-*l*
9×associate-/r*
7×associate-/l*
6×pow1
5×cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l/ add-log-exp
3×frac-2neg associate-*r* associate-*l/ prod-exp clear-num cbrt-unprod
2×unswap-sqr
1×flip3-- div-sub pow-prod-down *-commutative frac-sub flip-- sub-div
Counts
4 → 120
Calls
4 calls:
2.0ms
(/ y.im (hypot y.im y.re))
20.0ms
(/ (- (/ (* x.im y.re) (hypot y.im y.re)) (* (/ y.im (hypot y.im y.re)) x.re)) (hypot y.im y.re))
8.0ms
(* (/ y.im (hypot y.im y.re)) x.re)
4.0ms
(/ (* x.im y.re) (hypot y.im y.re))

series453.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ y.im (hypot y.im y.re))
230.0ms
(/ (- (/ (* x.im y.re) (hypot y.im y.re)) (* (/ y.im (hypot y.im y.re)) x.re)) (hypot y.im y.re))
93.0ms
(* (/ y.im (hypot y.im y.re)) x.re)
69.0ms
(/ (* x.im y.re) (hypot y.im y.re))

simplify528.0ms

Counts
132 → 132
Iterations

Useful iterations: 2 (122.0ms)

IterNodesCost
01771861
14161786
215881632
done50001632

prune339.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes95.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
11319
done1319

end0.0ms

sample495.0ms

Algorithm
intervals
Results
287.0ms8494×body80valid