Details

Time bar (total: 27.2s)

sample56.0ms

Algorithm
intervals
Results
40.0ms456×body80valid

simplify7.1s

Counts
1 → 1
Iterations

Useful iterations: 5 (299.0ms)

IterNodesCost
011362
123297
250297
3110297
4268257
5723203
61781203
74454203
done5000203

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.1b

localize20.0ms

Local error

Found 2 expressions with local error:

0.2b
(* 3 (* x.re x.re))
7.7b
(* (- (* 3 (* x.re x.re)) (* x.im x.im)) x.im)

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
8×add-sqr-sqrt
6×associate-*l*
5×*-un-lft-identity add-cube-cbrt
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u associate-*l/ *-commutative log1p-expm1-u add-log-exp unswap-sqr
1×flip3-- flip--
Counts
2 → 43
Calls
2 calls:
24.0ms
(* 3 (* x.re x.re))
94.0ms
(* (- (* 3 (* x.re x.re)) (* x.im x.im)) x.im)

series131.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* 3 (* x.re x.re))
91.0ms
(* (- (* 3 (* x.re x.re)) (* x.im x.im)) x.im)

simplify4.1s

Counts
49 → 49
Iterations

Useful iterations: 2 (241.0ms)

IterNodesCost
07911780
12039775
27049533
334629533
done50019533

prune270.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x.re x.im) (* x.im x.re))
0.2b
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
7.7b
(* (- (* x.re x.re) (* x.im x.im)) x.im)

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt associate-*l/
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
7×associate-*l*
6×associate-*r*
5×flip3-+ flip-+
4×expm1-log1p-u frac-add log1p-expm1-u
3×flip3-- flip--
2×+-commutative sum-log fma-def pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×difference-of-squares
Counts
4 → 77
Calls
4 calls:
7.0ms
(+ (* x.re x.im) (* x.im x.re))
24.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
18.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
31.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

series232.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* x.re x.im) (* x.im x.re))
90.0ms
(+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
36.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
77.0ms
(* (- (* x.re x.re) (* x.im x.im)) x.im)

simplify2.6s

Counts
89 → 89
Iterations

Useful iterations: done (2.6s)

IterNodesCost
014331443
142722640
2167921816
done500019728

prune537.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x.re x.im) (* x.im x.re))
0.2b
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
0.2b
(* (+ x.re x.im) (* (- x.re x.im) x.im))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
42×associate-*l/
20×flip3-+ flip-+
16×frac-add
12×frac-times
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity flip3-- flip--
8×add-log-exp
7×associate-*l* add-cube-cbrt
6×associate-*r/
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×+-commutative sum-log fma-def *-commutative
1×distribute-lft-out unswap-sqr
Counts
4 → 95
Calls
4 calls:
14.0ms
(+ (* x.re x.im) (* x.im x.re))
65.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
31.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
38.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

series311.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* x.re x.im) (* x.im x.re))
118.0ms
(+ (* (+ x.re x.im) (* (- x.re x.im) x.im)) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
38.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)
118.0ms
(* (+ x.re x.im) (* (- x.re x.im) x.im))

simplify3.2s

Counts
107 → 107
Iterations

Useful iterations: done (3.2s)

IterNodesCost
020555372
175037816
2403135489
done500035464

prune658.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x.re x.im) x.im)
0.0b
(+ (* x.re x.im) (* x.im x.re))
0.2b
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
0.2b
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r* add-log-exp
4×expm1-log1p-u associate-*l/ log1p-expm1-u
2×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
1×+-commutative sum-log fma-def flip3-- fma-udef flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 70
Calls
4 calls:
20.0ms
(* (- x.re x.im) x.im)
6.0ms
(+ (* x.re x.im) (* x.im x.re))
0.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
26.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

series240.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* (- x.re x.im) x.im)
31.0ms
(+ (* x.re x.im) (* x.im x.re))
131.0ms
(fma (+ x.re x.im) (* (- x.re x.im) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re))
25.0ms
(* (+ (* x.re x.im) (* x.im x.re)) x.re)

simplify4.7s

Counts
82 → 82
Iterations

Useful iterations: 3 (2.4s)

IterNodesCost
011420079
128014958
292614493
3377914229
done500014229

prune464.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

regimes236.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
010337
114297
done14297

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.3s14284×body80valid