Details

Time bar (total: 16.6s)

sample26.0ms

Algorithm
intervals
Results
13.0ms264×body80valid

simplify95.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize11.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (* x.im y.re) (* x.re y.im))
28.0b
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num div-inv
Counts
2 → 48
Calls
2 calls:
11.0ms
(- (* x.im y.re) (* x.re y.im))
25.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series182.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(- (* x.im y.re) (* x.re y.im))
137.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.7s

Counts
54 → 54
Iterations

Useful iterations: done (2.7s)

IterNodesCost
088931
1216906
2713807
32539807
done5000801

prune226.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.2b
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
1.2b
(- (* x.im y.re) (* x.re y.im))
18.9b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite103.0ms

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.re y.im)
56.0ms
(* (/ 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))
27.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series563.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(hypot y.re y.im)
285.0ms
(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
50.0ms
(- (* x.im y.re) (* x.re y.im))
171.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify1.9s

Counts
128 → 128
Iterations

Useful iterations: 2 (322.0ms)

IterNodesCost
01712225
14562076
215201817
done50001817

prune573.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
1.2b
(- (* x.im y.re) (* x.re y.im))
18.9b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite95.0ms

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.re y.im)
43.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
14.0ms
(- (* x.im y.re) (* x.re y.im))
33.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series475.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(hypot y.re y.im)
187.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
50.0ms
(- (* x.im y.re) (* x.re y.im))
180.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify2.8s

Counts
143 → 143
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01942874
14542796
212522600
344782545
done50002542

prune739.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.1b
(/ (- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im)))) (hypot y.re y.im))
7.0b
(* y.im (/ x.re (hypot y.re y.im)))
11.2b
(/ (* y.re x.im) (hypot y.re y.im))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity times-frac
16×add-exp-log add-cbrt-cube
13×associate-*r*
6×pow1 associate-/r*
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u associate-/l/ associate-/l* add-log-exp
3×associate-*r/ associate-*l* prod-exp cbrt-unprod div-inv
2×frac-2neg clear-num unswap-sqr
1×hypot-udef flip3-- div-sub pow-prod-down *-commutative frac-sub flip-- sub-div
Counts
4 → 101
Calls
4 calls:
0.0ms
(hypot y.re y.im)
59.0ms
(/ (- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im)))) (hypot y.re y.im))
38.0ms
(* y.im (/ x.re (hypot y.re y.im)))
12.0ms
(/ (* y.re x.im) (hypot y.re y.im))

series585.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(hypot y.re y.im)
302.0ms
(/ (- (/ (* y.re x.im) (hypot y.re y.im)) (* y.im (/ x.re (hypot y.re y.im)))) (hypot y.re y.im))
104.0ms
(* y.im (/ x.re (hypot y.re y.im)))
125.0ms
(/ (* y.re x.im) (hypot y.re y.im))

simplify2.8s

Counts
113 → 113
Iterations

Useful iterations: 2 (217.0ms)

IterNodesCost
01661651
13901571
212571433
348481433
done50001433

prune606.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes209.0ms

Accuracy

0% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 1.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: done (3.0ms)

IterNodesCost
01524
12021
done2019

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.2s8474×body80valid