Details

sample50.0ms

Algorithm

intervals

Results

23.0ms

283×

body

valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.1b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x.re y.re) (* x.im y.im))
24.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

12.0ms	(+ (* x.re y.re) (* x.im y.im))
72.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series157.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(+ (* x.re y.re) (* x.im y.im))
120.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify844.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
2	1059
1	248
0	90

prune439.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.1b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.re x.re (* x.im y.im))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
14.7b	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`*-un-lft-identity` `add-exp-log`
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`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

3 → 97

Calls

3 calls:

1.0ms	(fma y.re x.re (* x.im y.im))
47.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
8.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

series497.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(fma y.re x.re (* x.im y.im))
286.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im)))
136.0ms	(/ (fma y.re x.re (* x.im y.im)) (hypot y.re y.im))

simplify3.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	2911
1	373
0	139

prune722.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x.im y.im (* y.re x.re))
0.1b	(/ (/ (fma x.im y.im (* y.re x.re)) (hypot y.re y.im)) (hypot y.re y.im))
14.7b	(/ (fma x.im y.im (* y.re x.re)) (hypot y.re y.im))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

0.0ms	(fma x.im y.im (* y.re x.re))
18.0ms	(/ (/ (fma x.im y.im (* y.re x.re)) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms	(/ (fma x.im y.im (* y.re x.re)) (hypot y.re y.im))

series485.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma x.im y.im (* y.re x.re))
206.0ms	(/ (/ (fma x.im y.im (* y.re x.re)) (hypot y.re y.im)) (hypot y.re y.im))
221.0ms	(/ (fma x.im y.im (* y.re x.re)) (hypot y.re y.im))

simplify771.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	1669
1	351
0	160

prune971.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x.im y.im (* y.re x.re))
0.1b	(/ (/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))) (hypot y.re y.im))
0.2b	(/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re))))
14.7b	(/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 319

Calls

4 calls:

0.0ms	(fma x.im y.im (* y.re x.re))
32.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))) (hypot y.re y.im))
16.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re))))
8.0ms	(/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))

series758.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma x.im y.im (* y.re x.re))
273.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))) (hypot y.re y.im))
256.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re))))
172.0ms	(/ (hypot y.re y.im) (fma x.im y.im (* y.re x.re)))

simplify1.4s

Counts

331 → 331

Iterations

Iter	Nodes
done	5001
1	1310
0	458

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 1.3b

regimes483.0ms

Accuracy

30.2% (9.7b remaining)

Error of 11.9b against oracle of 2.2b and baseline of 16.1b

bsearch111.0ms

Steps

Iters	Range		Point
6	8.846670165818639e+179	1.1670387656327415e+181	1.7216921703264507e+180
8	-4.194746639390341e+188	-1.186401832632246e+184	-2.328453055309953e+184

simplify4.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample1.2s

Algorithm

intervals

Results

726.0ms

8478×

body

valid