Details

Time bar (total: 8.6s)

sample19.0ms

Algorithm
intervals
Results
9.0ms272×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11515
done1515

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(+ (* x.re y.re) (* x.im y.im))
27.9b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×pow1 associate-/r* associate-/l*
2×+-commutative sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 53
Calls
3 calls:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
11.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series141.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* y.re y.re) (* y.im y.im))
30.0ms
(+ (* x.re y.re) (* x.im y.im))
79.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts
62 → 62
Iterations

Useful iterations: 3 (670.0ms)

IterNodesCost
0991090
12701067
2931965
33227951
done5000951

prune185.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 27.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
16.8b
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
5×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 84
Calls
4 calls:
2.0ms
(+ (* x.re y.re) (* x.im y.im))
11.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series211.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* x.re y.re) (* x.im y.im))
105.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts
96 → 96
Iterations

Useful iterations: 3 (347.0ms)

IterNodesCost
01171780
12741657
27521557
320171527
done50001527

prune297.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.7b
(+ (* x.re y.re) (* x.im y.im))
27.9b
(/ (+ (* x.re y.re) (* x.im y.im)) (pow (+ (* y.re y.re) (* y.im y.im)) 1))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×times-frac
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
8×add-exp-log
7×associate-/r* add-log-exp
5×add-cbrt-cube
4×sqr-pow
3×pow1 flip3-+ div-exp flip-+ associate-/l*
2×+-commutative sum-log associate-/l/
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
3 → 69
Calls
3 calls:
2.0ms
(+ (* y.re y.re) (* y.im y.im))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
15.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (pow (+ (* y.re y.re) (* y.im y.im)) 1))

series135.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* y.re y.re) (* y.im y.im))
29.0ms
(+ (* x.re y.re) (* x.im y.im))
79.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (pow (+ (* y.re y.re) (* y.im y.im)) 1))

simplify1.9s

Counts
78 → 78
Iterations

Useful iterations: 3 (766.0ms)

IterNodesCost
01331716
13301525
211561377
349131363
done50001363

prune212.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow y.im 2) (pow y.re 2))
0.2b
(/ 1 (/ (+ (pow y.im 2) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im))))
0.7b
(+ (* y.re x.re) (* y.im x.im))
27.8b
(/ (+ (pow y.im 2) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
140×*-un-lft-identity
138×times-frac
72×add-sqr-sqrt add-cube-cbrt
34×unpow-prod-down distribute-lft-out
24×associate-/r*
17×add-exp-log
11×associate-/r/ add-cbrt-cube
8×flip3-+ div-exp flip-+ associate-/l* add-log-exp
6×div-inv
5×pow1
4×cbrt-undiv
2×+-commutative rec-exp frac-2neg 1-exp clear-num sum-log associate-/l/
1×pow-flip inv-pow
Counts
4 → 171
Calls
4 calls:
10.0ms
(+ (pow y.im 2) (pow y.re 2))
26.0ms
(/ 1 (/ (+ (pow y.im 2) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im))))
2.0ms
(+ (* y.re x.re) (* y.im x.im))
30.0ms
(/ (+ (pow y.im 2) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (pow y.im 2) (pow y.re 2))
140.0ms
(/ 1 (/ (+ (pow y.im 2) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im))))
34.0ms
(+ (* y.re x.re) (* y.im x.im))
64.0ms
(/ (+ (pow y.im 2) (pow y.re 2)) (+ (* y.re x.re) (* y.im x.im)))

simplify949.0ms

Counts
183 → 183
Iterations

Useful iterations: 2 (304.0ms)

IterNodesCost
02144572
15314206
215823829
done50003829

prune353.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.4b

regimes171.0ms

Accuracy

-11% (3.3b remaining)

Error of 26.9b against oracle of 23.6b and baseline of 26.5b

bsearch83.0ms

Steps
ItersRangePoint
8
7.2003153639421815e+143
1.3871548251723246e+147
1.3021609369269456e+147
9
4.0573096534452066e+47
2.7287424349260767e+55
2.666479014498774e+55

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03060
13560
done3560

end0.0ms

sample514.0ms

Algorithm
intervals
Results
302.0ms8471×body80valid