Details

Time bar (total: 8.4s)

sample24.0ms

Algorithm
intervals
Results
12.0ms277×body80valid

simplify31.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11915
23615
34815
46615
57215
done7215

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 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)) (+ (* y.re y.re) (* y.im y.im)))

rewrite19.0ms

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:
3.0ms
(+ (* y.re y.re) (* y.im y.im))
3.0ms
(- (* x.im y.re) (* x.re y.im))
12.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series148.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* 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)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts
64 → 64
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
01021120
12891097
21062981
34742981
done5000981

prune174.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 26.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* x.im y.re) (* x.re y.im))
15.5b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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:
2.0ms
(- (* x.im y.re) (* x.re y.im))
13.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* x.im y.re) (* x.re y.im))
111.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.1s

Counts
98 → 98
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01211814
13041682
28731574
328181558
done50001557

prune292.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.1b

localize14.0ms

Local error

Found 4 expressions with local error:

9.2b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
585×sqrt-prod
567×times-frac
302×add-sqr-sqrt
299×add-cube-cbrt *-un-lft-identity
50×sqrt-div
33×associate-/l*
22×associate-/r/
14×flip3-+ flip-+
11×div-inv
9×add-exp-log associate-/r* add-cbrt-cube
7×pow1
4×add-log-exp
3×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
2×div-sub
1×frac-2neg clear-num associate-/l/
Counts
4 → 402
Calls
4 calls:
34.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts
414 → 414
Iterations

Useful iterations: done (994.0ms)

IterNodesCost
043620421
1102318015
2251916855
done500116853

prune740.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.1b

localize28.0ms

Local error

Found 4 expressions with local error:

29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.7b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.8b
(cbrt (+ (* y.re y.re) (* y.im y.im)))
30.8b
(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
2.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
2.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
94.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
95.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify781.0ms

Counts
68 → 68
Iterations

Useful iterations: 3 (214.0ms)

IterNodesCost
065890
1144824
2387716
31354710
done5000710

prune378.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.1b

regimes170.0ms

Accuracy

-5.8% (3.1b remaining)

Error of 26.8b against oracle of 23.7b and baseline of 26.7b

bsearch54.0ms

Steps
ItersRangePoint
10
6.409730244873951e+265
3.5402997186520582e+277
2.966297851011323e+277

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01840
12340
done2340

end0.0ms

sample521.0ms

Algorithm
intervals
Results
303.0ms8494×body80valid