Details

sample42.0ms

Algorithm

intervals

Results

24.0ms

270×

body

valid

simplify79.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.im y.im (* y.re y.re))
1.1b	(- (* x.im y.re) (* x.re y.im))
24.0b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

rewrite42.0ms

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))
17.0ms	(- (* 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)))

series195.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma y.im y.im (* y.re y.re))
43.0ms	(- (* x.im y.re) (* x.re y.im))
116.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.im y.im (* y.re y.re)))

simplify2.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	3282
2	839
1	235
0	99

prune439.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 23.5b

localize25.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
16.4b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.2b	(sqrt (fma y.im y.im (* y.re y.re)))
28.2b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite65.0ms

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:

18.0ms	(- (* x.im y.re) (* x.re y.im))
36.0ms	(/ (- (* 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)))
6.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* x.im y.re) (* x.re y.im))
187.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
68.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
86.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
3	2132
2	759
1	270
0	117

prune767.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.4b

localize31.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
16.6b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
28.2b	(sqrt (fma y.im y.im (* y.re y.re)))
28.2b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-l` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `cbrt-unprod` `fma-udef` `hypot-def`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `fma-neg` `diff-log` `1-exp` `prod-diff` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 105

Calls

4 calls:

9.0ms	(- (* x.im y.re) (* x.re y.im))
73.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (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)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* x.im y.re) (* x.re y.im))
181.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
67.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
62.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.9s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
3	3063
2	893
1	339
0	142

prune660.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.4b

localize38.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
16.5b	(/ (sqrt (fma y.im y.im (* y.re y.re))) (- (* x.im y.re) (* x.re y.im)))
28.2b	(sqrt (fma y.im y.im (* y.re y.re)))
28.2b	(sqrt (fma y.im y.im (* y.re y.re)))

rewrite47.0ms

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*` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `fma-udef` `hypot-def` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-exp` `prod-diff` `div-inv`

Counts

4 → 95

Calls

4 calls:

16.0ms	(- (* x.im y.re) (* x.re y.im))
20.0ms	(/ (sqrt (fma y.im y.im (* y.re y.re))) (- (* x.im y.re) (* x.re y.im)))
7.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* x.im y.re) (* x.re y.im))
155.0ms	(/ (sqrt (fma y.im y.im (* y.re y.re))) (- (* x.im y.re) (* x.re y.im)))
59.0ms	(sqrt (fma y.im y.im (* y.re y.re)))
62.0ms	(sqrt (fma y.im y.im (* y.re y.re)))

simplify3.9s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
4	4940
3	1647
2	626
1	232
0	112

prune671.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 22.4b

regimes374.0ms

Accuracy

0% (2.4b remaining)

Error of 25.1b against oracle of 22.7b and baseline of 25.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	14

end0.0ms

sample951.0ms

Algorithm

intervals

Results

704.0ms

8466×

body

valid