Details

sample33.0ms

Algorithm

intervals

Results

15.0ms

272×

body

valid

simplify54.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x.im y.re) (* x.re y.im))
23.2b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite23.0ms

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` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

2 → 48

Calls

2 calls:

7.0ms	(- (* x.im y.re) (* x.re y.im))
15.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series146.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (* x.im y.re) (* x.re y.im))
104.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify2.0s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
3	3623
2	800
1	221
0	88

prune300.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
14.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
27.1b	(sqrt (fma y.im y.im (* y.re y.re)))
27.1b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`*-un-lft-identity` `add-cube-cbrt`
150×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def`
1×	`flip3--` `flip--`

Counts

4 → 254

Calls

4 calls:

22.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
16.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
199.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
47.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
59.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.6s

Counts

266 → 266

Iterations

Iter	Nodes
done	5000
2	3353
1	678
0	273

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.3b

localize47.0ms

Local error

Found 4 expressions with local error:

27.1b	(sqrt (fma y.im y.im (* y.re y.re)))
27.1b	(sqrt (fma y.im y.im (* y.re y.re)))
27.1b	(sqrt (fma y.im y.im (* y.re y.re)))
27.1b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `fma-udef` `hypot-def` `log1p-expm1-u` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
1.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
63.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
76.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
68.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
8	1004
7	371
6	191
5	115
4	81
3	64
2	46
1	34
0	24

prune546.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.3b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* y.re x.im) (* y.im x.re))
0.6b	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* y.re x.im) (* y.im x.re))))
22.8b	(/ (fma y.im y.im (* y.re y.re)) (- (* y.re x.im) (* y.im x.re)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-flip` `inv-pow`

Counts

3 → 133

Calls

3 calls:

7.0ms	(- (* y.re x.im) (* y.im x.re))
23.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* y.re x.im) (* y.im x.re))))
19.0ms	(/ (fma y.im y.im (* y.re y.re)) (- (* y.re x.im) (* y.im x.re)))

series388.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(- (* y.re x.im) (* y.im x.re))
216.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* y.re x.im) (* y.im x.re))))
120.0ms	(/ (fma y.im y.im (* y.re y.re)) (- (* y.re x.im) (* y.im x.re)))

simplify1.8s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
2	2505
1	480
0	194

prune820.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.5b

regimes372.0ms

Accuracy

0% (2.8b remaining)

Error of 17.0b against oracle of 14.2b and baseline of 17.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	17
1	17
0	12

end0.0ms

sample1.3s

Algorithm

intervals

Results

763.0ms

8438×

body

valid