Details

Time bar (total: 16.4s)

sample27.0ms

Algorithm
intervals
Results
14.0ms272×body80valid

simplify40.0ms

Counts
1 → 1
Iterations
IterNodes
done70
570
466
348
236
119
011

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.0b
(- (* x.im y.re) (* x.re y.im))
27.7b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
3×pow1 associate-/r* associate-/l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
3 → 55
Calls
3 calls:
6.0ms
(+ (* y.re y.re) (* y.im y.im))
6.0ms
(- (* x.im y.re) (* x.re y.im))
30.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series206.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(+ (* y.re y.re) (* y.im y.im))
49.0ms
(- (* x.im y.re) (* x.re y.im))
115.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.4s

Counts
64 → 64
Iterations
IterNodes
done5066
34560
21132
1304
0101

prune325.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
17.2b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×*-un-lft-identity add-cube-cbrt
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×flip3-+ add-cbrt-cube add-exp-log flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×flip3-- flip--
Counts
4 → 266
Calls
4 calls:
52.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
25.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series379.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
170.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
59.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.2s

Counts
278 → 278
Iterations
IterNodes
done5000
22095
1741
0307

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.3b

localize40.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ x.re (/ (+ (* y.re y.re) (* y.im y.im)) y.im))
7.9b
(/ (+ (* y.re y.re) (* y.im y.im)) x.im)
12.4b
(/ y.re (/ (+ (* y.re y.re) (* y.im y.im)) x.im))
18.4b
(/ (+ (* y.re y.re) (* y.im y.im)) y.im)

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
168×times-frac
104×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
32×associate-/r*
18×add-cbrt-cube add-exp-log
12×div-inv associate-/l*
8×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg add-log-exp associate-/l/
2×flip3-+ associate-/r/ flip-+
Counts
4 → 198
Calls
4 calls:
15.0ms
(/ x.re (/ (+ (* y.re y.re) (* y.im y.im)) y.im))
25.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) x.im)
16.0ms
(/ y.re (/ (+ (* y.re y.re) (* y.im y.im)) x.im))
26.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) y.im)

series290.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ x.re (/ (+ (* y.re y.re) (* y.im y.im)) y.im))
54.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) x.im)
98.0ms
(/ y.re (/ (+ (* y.re y.re) (* y.im y.im)) x.im))
54.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) y.im)

simplify1.9s

Counts
210 → 210
Iterations
IterNodes
done5002
22680
1818
0314

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.6b

localize37.0ms

Local error

Found 4 expressions with local error:

3.3b
(/ x.re (+ y.im (/ (* y.re y.re) y.im)))
6.0b
(/ (* y.re y.re) y.im)
7.9b
(/ (+ (* y.re y.re) (* y.im y.im)) x.im)
12.4b
(/ y.re (/ (+ (* y.re y.re) (* y.im y.im)) x.im))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
99×times-frac
73×*-un-lft-identity
65×add-sqr-sqrt add-cube-cbrt
23×associate-/r*
18×add-cbrt-cube add-exp-log
10×associate-/l*
8×div-inv
7×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg distribute-lft-out add-log-exp
3×associate-/r/
2×flip3-+ flip-+ associate-/l/
1×prod-exp cbrt-unprod
Counts
4 → 153
Calls
4 calls:
17.0ms
(/ x.re (+ y.im (/ (* y.re y.re) y.im)))
10.0ms
(/ (* y.re y.re) y.im)
25.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) x.im)
12.0ms
(/ y.re (/ (+ (* y.re y.re) (* y.im y.im)) x.im))

series265.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ x.re (+ y.im (/ (* y.re y.re) y.im)))
26.0ms
(/ (* y.re y.re) y.im)
74.0ms
(/ (+ (* y.re y.re) (* y.im y.im)) x.im)
104.0ms
(/ y.re (/ (+ (* y.re y.re) (* y.im y.im)) x.im))

simplify1.6s

Counts
165 → 165
Iterations
IterNodes
done5000
22278
1674
0261

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.5b

regimes459.0ms

Accuracy

16.3% (5.2b remaining)

Error of 14.8b against oracle of 9.6b and baseline of 15.8b

bsearch134.0ms

Steps
ItersRangePoint
8
6.213657247597489e-163
1.6114349507042464e-160
1.0301939902596996e-162
9
-8.897020078895062e+156
-7.498175397658886e+147
-2.0204915446540252e+153

simplify6.0ms

Iterations
IterNodes
done42
142
036

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s8484×body80valid