Details

sample152.0ms

Algorithm

intervals

Results

57.0ms	256×	body	80	valid
49.0ms	252×	body	80	nan

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
2	32
1	27
0	18

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.5b	(* (log base) (log base))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
17×	`pow1`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `associate-/l`
1×	`pow2` `cbrt-undiv` `hypot-udef` `clear-num` `frac-2neg` `pow-plus` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot re im)
8.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
1.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
18.0ms	(* (log base) (log base))

series978.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot re im)
461.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
243.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
222.0ms	(* (log base) (log base))

simplify2.1s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
3	2007
2	793
1	305
0	148

prune893.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`pow1`
18×	`times-frac`
12×	`log-prod` `swap-sqr` `log-pow` `sqrt-prod`
10×	`add-cbrt-cube` `add-exp-log`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `associate-/r*` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 127

Calls

4 calls:

10.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
16.0ms	(* (log base) (log base))
13.0ms	(* (log base) (log base))

series1.1s

Counts

4 → 12

Calls

4 calls:

489.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
193.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
224.0ms	(* (log base) (log base))
218.0ms	(* (log base) (log base))

simplify2.2s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	1961
2	761
1	309
0	153

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.6b	(cbrt base)
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series914.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
264.0ms	(cbrt base)
235.0ms	(cbrt base)
261.0ms	(cbrt base)

simplify1.5s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
4	1584
3	470
2	191
1	100
0	59

prune728.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.5b	(* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
0.5b	(* (log base) (log base))
0.6b	(cbrt (* (* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`swap-sqr`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-r` `associate-l`
6×	`log-prod` `log-pow`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 89

Calls

4 calls:

0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
6.0ms	(* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
8.0ms	(* (log base) (log base))
11.0ms	(cbrt (* (* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))

series925.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
314.0ms	(* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
232.0ms	(* (log base) (log base))
181.0ms	(cbrt (* (* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))

simplify2.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
3	1998
2	695
1	264
0	121

prune784.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0b

regimes593.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
1.2s	7931×	body	80	nan