Details

Time bar (total: 11.0s)

sample32.0ms

Algorithm
intervals
Results
14.0ms262×body80valid

simplify77.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01115
11915
23615
34815
46615
57215
done7215

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.3b
(- (* x.im y.re) (* x.re y.im))
24.3b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite82.0ms

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
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
16.0ms
(+ (* y.re y.re) (* y.im y.im))
15.0ms
(- (* x.im y.re) (* x.re y.im))
49.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series235.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(+ (* y.re y.re) (* y.im y.im))
58.0ms
(- (* x.im y.re) (* x.re y.im))
137.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts
64 → 64
Iterations

Useful iterations: 2 (244.0ms)

IterNodesCost
01021120
13201097
21796983
done5000983

prune236.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* x.im y.re) (* x.re y.im))
14.7b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite115.0ms

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
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
17.0ms
(- (* x.im y.re) (* x.re y.im))
64.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
11.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (* x.im y.re) (* x.re y.im))
198.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
69.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
66.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify841.0ms

Counts
98 → 98
Iterations

Useful iterations: done (836.0ms)

IterNodesCost
01211814
13131682
212191576
done50001574

prune581.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.3b
(- (* x.im y.re) (* x.re y.im))
0.6b
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
23.8b
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×add-cube-cbrt times-frac
17×add-exp-log
15×associate-*r*
11×add-cbrt-cube
8×add-log-exp
7×pow1
4×div-exp prod-exp associate-/r/
3×flip3-- flip3-+ associate-*l* associate-/r* flip-- flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×+-commutative sub-neg pow-flip frac-2neg diff-log associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 98
Calls
4 calls:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(- (* x.im y.re) (* x.re y.im))
23.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
60.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series324.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* y.re y.re) (* y.im y.im))
75.0ms
(- (* x.im y.re) (* x.re y.im))
73.0ms
(/ 1 (+ (* y.re y.re) (* y.im y.im)))
142.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify3.4s

Counts
110 → 110
Iterations

Useful iterations: 2 (579.0ms)

IterNodesCost
01411797
14221682
230771431
done50011431

prune332.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.3b
(- (* x.im y.re) (* x.re y.im))
24.3b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite77.0ms

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
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
17.0ms
(+ (* y.re y.re) (* y.im y.im))
17.0ms
(- (* x.im y.re) (* x.re y.im))
40.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series274.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ (* y.re y.re) (* y.im y.im))
63.0ms
(- (* x.im y.re) (* x.re y.im))
156.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts
64 → 64
Iterations

Useful iterations: 2 (274.0ms)

IterNodesCost
01021120
13201097
21796983
done5000983

prune276.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 21.3b

regimes202.0ms

Accuracy

9.4% (2.8b remaining)

Error of 26.2b against oracle of 23.4b and baseline of 26.4b

bsearch3.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01853
12153
done2153

end0.0ms

sample1.1s

Algorithm
intervals
Results
677.0ms8444×body80valid