Details

sample43.0ms

Algorithm

intervals

Results

23.0ms

265×

body

valid

simplify34.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	72
5	72
4	66
3	48
2	36
1	19
0	11

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.4b	(- (* x.im y.re) (* x.re y.im))
29.3b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite76.0ms

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:

11.0ms	(+ (* y.re y.re) (* y.im y.im))
12.0ms	(- (* x.im y.re) (* x.re y.im))
50.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series254.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(+ (* y.re y.re) (* y.im y.im))
56.0ms	(- (* x.im y.re) (* x.re y.im))
140.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify940.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	1834
1	319
0	101

prune417.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 25.1b

localize31.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ x.im (/ (+ (* y.im y.im) (* y.re y.re)) y.re))
4.6b	(/ x.re (/ (+ (* y.im y.im) (* y.re y.re)) y.im))
17.7b	(/ (+ (* y.im y.im) (* y.re y.re)) y.im)
18.0b	(/ (+ (* y.im y.im) (* y.re y.re)) y.re)

rewrite124.0ms

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:

24.0ms	(/ x.im (/ (+ (* y.im y.im) (* y.re y.re)) y.re))
30.0ms	(/ x.re (/ (+ (* y.im y.im) (* y.re y.re)) y.im))
36.0ms	(/ (+ (* y.im y.im) (* y.re y.re)) y.im)
20.0ms	(/ (+ (* y.im y.im) (* y.re y.re)) y.re)

series291.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ x.im (/ (+ (* y.im y.im) (* y.re y.re)) y.re))
68.0ms	(/ x.re (/ (+ (* y.im y.im) (* y.re y.re)) y.im))
75.0ms	(/ (+ (* y.im y.im) (* y.re y.re)) y.im)
82.0ms	(/ (+ (* y.im y.im) (* y.re y.re)) y.re)

simplify1.6s

Counts

210 → 210

Iterations

Iter	Nodes
done	5001
2	4397
1	831
0	314

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.5b

localize25.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ x.im (+ y.re (/ (* y.im y.im) y.re)))
4.6b	(/ x.re (/ (+ (* y.im y.im) (* y.re y.re)) y.im))
4.9b	(/ (* y.im y.im) y.re)
17.7b	(/ (+ (* y.im y.im) (* y.re y.re)) y.im)

rewrite120.0ms

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:

26.0ms	(/ x.im (+ y.re (/ (* y.im y.im) y.re)))
31.0ms	(/ x.re (/ (+ (* y.im y.im) (* y.re y.re)) y.im))
15.0ms	(/ (* y.im y.im) y.re)
38.0ms	(/ (+ (* y.im y.im) (* y.re y.re)) y.im)

series232.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ x.im (+ y.re (/ (* y.im y.im) y.re)))
79.0ms	(/ x.re (/ (+ (* y.im y.im) (* y.re y.re)) y.im))
37.0ms	(/ (* y.im y.im) y.re)
77.0ms	(/ (+ (* y.im y.im) (* y.re y.re)) y.im)

simplify2.1s

Counts

165 → 165

Iterations

Iter	Nodes
done	5001
2	4235
1	693
0	261

prune942.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize23.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ x.im (+ y.re (/ (* y.im y.im) y.re)))
4.6b	(/ x.re (+ (/ (* y.re y.re) y.im) y.im))
4.9b	(/ (* y.im y.im) y.re)
6.4b	(/ (* y.re y.re) y.im)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
30×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r*`
8×	`distribute-lft-out` `associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `associate-/r/` `div-inv` `add-log-exp`
2×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 108

Calls

4 calls:

24.0ms	(/ x.im (+ y.re (/ (* y.im y.im) y.re)))
36.0ms	(/ x.re (+ (/ (* y.re y.re) y.im) y.im))
15.0ms	(/ (* y.im y.im) y.re)
13.0ms	(/ (* y.re y.re) y.im)

series167.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ x.im (+ y.re (/ (* y.im y.im) y.re)))
57.0ms	(/ x.re (+ (/ (* y.re y.re) y.im) y.im))
24.0ms	(/ (* y.im y.im) y.re)
39.0ms	(/ (* y.re y.re) y.im)

simplify2.0s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	4163
1	495
0	187

prune681.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

regimes481.0ms

Accuracy

41.4% (1.9b remaining)

Error of 4.3b against oracle of 2.4b and baseline of 5.7b

bsearch96.0ms

Steps

Iters	Range		Point
7	5.161862198782221e-17	1.225336370434346e-14	1.310939369483502e-16
7	-938.9819325385033	-22.455199697559465	-61.106078959908636

simplify3.0ms

Iterations

Iter	Nodes
done	35
1	35
0	27

end0.0ms

sample1.2s

Algorithm

intervals

Results

759.0ms

8523×

body

valid