Details

sample56.0ms

Algorithm

intervals

Results

38.0ms

264×

body

valid

simplify92.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.2b	(- (* x.im y.re) (* x.re y.im))
28.8b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `fma-udef` `div-inv`

Counts

3 → 61

Calls

3 calls:

0.0ms	(fma y.im y.im (* y.re y.re))
13.0ms	(- (* x.im y.re) (* x.re y.im))
34.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series225.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(fma y.im y.im (* y.re y.re))
57.0ms	(- (* x.im y.re) (* x.re y.im))
115.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify986.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1086
1	235
0	99

prune357.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 28.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
18.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `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

4 → 96

Calls

4 calls:

13.0ms	(- (* x.im y.re) (* x.re y.im))
29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* x.im y.re) (* x.re y.im))
117.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
46.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
51.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify971.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1031
1	270
0	117

prune615.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma x.im y.re (- (* x.re y.im)))
18.9b	(/ (fma x.im y.re (- (* x.re y.im))) (sqrt (fma y.im y.im (* y.re y.re))))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma x.im y.re (- (* x.re y.im)))
8.0ms	(/ (fma x.im y.re (- (* x.re y.im))) (sqrt (fma y.im y.im (* y.re y.re))))
7.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma x.im y.re (- (* x.re y.im)))
124.0ms	(/ (fma x.im y.re (- (* x.re y.im))) (sqrt (fma y.im y.im (* y.re y.re))))
66.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
60.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.1s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
3	1672
2	411
1	148
0	95

prune509.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma x.im y.re (- (* x.re y.im)))
18.9b	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.im y.re (- (* x.re y.im))))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))
28.5b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `fma-udef`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma x.im y.re (- (* x.re y.im)))
8.0ms	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.im y.re (- (* x.re y.im))))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(fma x.im y.re (- (* x.re y.im)))
116.0ms	(/ (sqrt (fma y.im y.im (* y.re y.re))) (fma x.im y.re (- (* x.re y.im))))
64.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
55.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.3s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
3	1585
2	398
1	145
0	92

prune550.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.8b

regimes335.0ms

Accuracy

-9.7% (3.0b remaining)

Error of 26.2b against oracle of 23.2b and baseline of 25.9b

bsearch136.0ms

Steps

Iters	Range		Point
4	2.99988769581893e+36	5.314606313626179e+36	5.2422713568197025e+36
9	-3.137566432904386e+97	-7.171553699074835e+91	-1.2109434524169916e+96

simplify5.0ms

Iterations

Iter	Nodes
done	29
2	29
1	27
0	21

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8412×

body

valid