Details

sample53.0ms

Algorithm

intervals

Results

25.0ms

264×

body

valid

simplify261.0ms

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize112.0ms

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)))

rewrite92.0ms

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:

1.0ms	(fma y.im y.im (* y.re y.re))
24.0ms	(- (* x.im y.re) (* x.re y.im))
63.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

series439.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(fma y.im y.im (* y.re y.re))
102.0ms	(- (* x.im y.re) (* x.re y.im))
251.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify4.9s

Counts

70 → 70

Iterations

Iter	Nodes
done	5016
3	3076
2	863
1	235
0	99

prune980.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 28.6b

localize103.0ms

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)))

rewrite94.0ms

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:

25.0ms	(- (* x.im y.re) (* x.re y.im))
48.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
9.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
7.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (* x.im y.re) (* x.re y.im))
281.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
73.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
72.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify4.0s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
3	2063
2	743
1	269
0	117

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.9b

localize111.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
0.3b	(fma x.im y.re (- (* x.re y.im)))
28.8b	(/ (fma x.im y.re (- (* x.re y.im))) (fma y.im y.im (* y.re y.re)))

rewrite22.0ms

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`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 52

Calls

3 calls:

1.0ms	(fma y.im y.im (* y.re y.re))
1.0ms	(fma x.im y.re (- (* x.re y.im)))
17.0ms	(/ (fma x.im y.re (- (* x.re y.im))) (fma y.im y.im (* y.re y.re)))

series434.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma y.im y.im (* y.re y.re))
82.0ms	(fma x.im y.re (- (* x.re y.im)))
287.0ms	(/ (fma x.im y.re (- (* x.re y.im))) (fma y.im y.im (* y.re y.re)))

simplify6.2s

Counts

61 → 61

Iterations

Iter	Nodes
done	5018
4	3173
3	808
2	281
1	123
0	77

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.9b

localize131.0ms

Local error

Found 4 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))
0.3b	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
28.7b	(/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 147

Calls

4 calls:

2.0ms	(fma y.im y.im (* y.re y.re))
26.0ms	(- (* x.im y.re) (* x.re y.im))
81.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
36.0ms	(/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))

series654.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma y.im y.im (* y.re y.re))
74.0ms	(- (* x.im y.re) (* x.re y.im))
342.0ms	(/ 1 (/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im))))
178.0ms	(/ (fma y.im y.im (* y.re y.re)) (- (* x.im y.re) (* x.re y.im)))

simplify8.2s

Counts

159 → 159

Iterations

Iter	Nodes
done	5000
3	4435
2	1468
1	491
0	208

prune2.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 15.7b

regimes1.3s

Accuracy

-10.9% (3.5b remaining)

Error of 17.6b against oracle of 14.1b and baseline of 17.3b

bsearch116.0ms

Steps

Iters	Range		Point
8	-7.171553699074835e+91	-1.194776095236265e+88	-7.011154002702933e+91
6	-7.828969379025143e+161	-1.2817277478091954e+161	-1.304579087607779e+161

simplify12.0ms

Iterations

Iter	Nodes
done	33
1	33
0	23

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s

8412×

body

valid