Details

sample60.0ms

Algorithm

intervals

Results

40.0ms

271×

body

valid

simplify98.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	80
5	80
4	76
3	56
2	40
1	21
0	11

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize24.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
24.9b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite40.0ms

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--` `insert-posit16` `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 → 50

Calls

2 calls:

16.0ms	(- (* x.im y.re) (* x.re y.im))
23.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series196.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(- (* x.im y.re) (* x.re y.im))
127.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify831.0ms

Counts

56 → 56

Iterations

Iter	Nodes
3	2455
2	716
1	222
0	90

prune654.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
15.7b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
29.1b	(sqrt (fma y.im y.im (* y.re y.re)))
29.1b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite54.0ms

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:

8.0ms	(- (* x.im y.re) (* x.re y.im))
39.0ms	(/ (- (* 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)))
3.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* x.im y.re) (* x.re y.im))
169.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
67.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
63.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify640.0ms

Counts

108 → 108

Iterations

Iter	Nodes
3	2058
2	728
1	269
0	117

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
0.7b	(- (* x.im y.re) (* x.re y.im))
15.7b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
29.1b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 183

Calls

4 calls:

20.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
8.0ms	(- (* x.im y.re) (* x.re y.im))
36.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
3.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (sqrt (fma y.im y.im (* y.re y.re))))
52.0ms	(- (* x.im y.re) (* x.re y.im))
188.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))
87.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.2s

Counts

195 → 195

Iterations

Iter	Nodes
3	5275
2	1592
1	589
0	258

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.7b	(- (* x.im y.re) (* x.re y.im))
15.7b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

rewrite55.0ms

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`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `log1p-expm1-u` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 124

Calls

3 calls:

19.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
8.0ms	(- (* x.im y.re) (* x.re y.im))
26.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

series369.0ms

Counts

3 → 9

Calls

3 calls:

164.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re)) (hypot y.im y.re))
48.0ms	(- (* x.im y.re) (* x.re y.im))
157.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.im y.re))

simplify2.5s

Counts

133 → 133

Iterations

Iter	Nodes
3	5361
2	1455
1	457
0	190

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

regimes319.0ms

Accuracy

29.6% (7.4b remaining)

Error of 13.3b against oracle of 5.9b and baseline of 16.4b

bsearch177.0ms

Steps

Iters	Range		Point
11	1.372435673101672e+77	2.0708857304685872e+98	9.416337464243763e+96
9	-1.6413568746994335e+226	-5.008279408532683e+219	-5.1870879849634226e+219

simplify3.0ms

Iterations

Iter	Nodes
2	24
1	24
0	21

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.3s

8462×

body

valid