Details

sample42.0ms

Algorithm

intervals

Results

19.0ms

267×

body

valid

simplify112.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	11	15
1	21	14
2	40	14
3	56	14
4	76	14
5	90	14
6	94	14
done	94	14

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
25.2b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `div-inv`

Counts

2 → 48

Calls

2 calls:

14.0ms	(- (* x.im y.re) (* x.re y.im))
21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series194.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (* x.im y.re) (* x.re y.im))
135.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.1s

Counts

54 → 54

Iterations

Useful iterations: 3 (896.0ms)

Iter	Nodes	Cost
0	88	931
1	222	906
2	890	809
3	4246	807
done	5000	807

prune180.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.3b	(- (* x.im y.re) (* x.re y.im))
16.2b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`add-exp-log` `*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `add-log-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 106

Calls

3 calls:

40.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
9.0ms	(- (* x.im y.re) (* x.re y.im))
22.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series417.0ms

Counts

3 → 9

Calls

3 calls:

229.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
41.0ms	(- (* x.im y.re) (* x.re y.im))
147.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify1.7s

Counts

115 → 115

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	164	2165
1	489	2030
2	2387	1779
done	5000	1765

prune505.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.re y.im)) (hypot y.re y.im))
16.2b	(/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.re y.im))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 101

Calls

2 calls:

11.0ms	(/ (/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.re y.im)) (hypot y.re y.im))
5.0ms	(/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.re y.im))

series415.0ms

Counts

2 → 6

Calls

2 calls:

220.0ms	(/ (/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.re y.im)) (hypot y.re y.im))
195.0ms	(/ (fma x.re (- y.im) (* y.re x.im)) (hypot y.re y.im))

simplify1.0s

Counts

107 → 107

Iterations

Useful iterations: done (999.0ms)

Iter	Nodes	Cost
0	155	2536
1	343	2477
2	1599	2310
done	5002	2268

prune564.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ 1 (/ (hypot y.re y.im) (fma x.re (- y.im) (* y.re x.im)))) (hypot y.re y.im))
0.2b	(/ 1 (/ (hypot y.re y.im) (fma x.re (- y.im) (* y.re x.im))))
16.2b	(/ (hypot y.re y.im) (fma x.re (- y.im) (* y.re x.im)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
238×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
50×	`associate-/l*`
35×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
19×	`associate-/r*` `add-cbrt-cube`
10×	`cbrt-undiv`
5×	`associate-/r/`
4×	`pow1` `rec-exp` `1-exp`
3×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `associate-/l/` `inv-pow`

Counts

3 → 309

Calls

3 calls:

41.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.re (- y.im) (* y.re x.im)))) (hypot y.re y.im))
21.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re (- y.im) (* y.re x.im))))
8.0ms	(/ (hypot y.re y.im) (fma x.re (- y.im) (* y.re x.im)))

series669.0ms

Counts

3 → 9

Calls

3 calls:

247.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.re (- y.im) (* y.re x.im)))) (hypot y.re y.im))
262.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re (- y.im) (* y.re x.im))))
160.0ms	(/ (hypot y.re y.im) (fma x.re (- y.im) (* y.re x.im)))

simplify1.0s

Counts

318 → 318

Iterations

Useful iterations: done (992.0ms)

Iter	Nodes	Cost
0	454	9184
1	1312	8350
done	5001	7836

prune905.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.4b

regimes314.0ms

Accuracy

29.8% (10.3b remaining)

Error of 12.5b against oracle of 2.2b and baseline of 16.9b

bsearch99.0ms

Steps

Iters	Range		Point
7	1.821547073792465e+115	6.050378771870372e+116	2.9468590428583657e+116
7	-1.5593098650405636e+174	-7.484363023265762e+171	-8.854189588374422e+171

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	21	36
1	26	34
2	27	34
done	27	34

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s

8438×

body

valid