Details

sample154.0ms

Algorithm

intervals

Results

61.0ms	264×	body	80	nan
44.0ms	256×	body	80	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	33
2	33
1	27
0	18

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize55.0ms

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

rewrite15.0ms

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)
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
4.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
8.0ms	(* (log base) (log base))

series1.3s

Counts

4 → 12

Calls

4 calls:

68.0ms	(hypot re im)
248.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
430.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
516.0ms	(* (log base) (log base))

simplify1.6s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	1569
1	306
0	148

prune716.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.3b	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 263

Calls

4 calls:

0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
14.0ms	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
8.0ms	(* (log base) (log base))
7.0ms	(* (log base) (log base))

series1.0s

Counts

4 → 12

Calls

4 calls:

202.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
425.0ms	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
200.0ms	(* (log base) (log base))
210.0ms	(* (log base) (log base))

simplify2.4s

Counts

275 → 275

Iterations

Iter	Nodes
done	5001
2	4207
1	762
0	322

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log base) (log (hypot re im)))
0.3b	(/ (/ (+ (* (log base) (log (hypot re im))) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.6b	(* (log base) (log base))
0.6b	(* (log base) (log base))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
163×	`add-sqr-sqrt`
161×	`*-un-lft-identity`
157×	`add-cube-cbrt`
132×	`sqrt-prod`
34×	`pow1`
22×	`associate-/l*`
18×	`log-prod`
15×	`add-cbrt-cube` `add-exp-log`
14×	`log-pow`
12×	`swap-sqr` `associate-r` `associate-l`
9×	`distribute-rgt-in` `distribute-lft-in`
8×	`div-inv`
6×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`pow2` `pow-plus` `pow-sqr` `pow-prod-up`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 281

Calls

4 calls:

10.0ms	(* (log base) (log (hypot re im)))
28.0ms	(/ (/ (+ (* (log base) (log (hypot re im))) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
8.0ms	(* (log base) (log base))
8.0ms	(* (log base) (log base))

series1.0s

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (log base) (log (hypot re im)))
417.0ms	(/ (/ (+ (* (log base) (log (hypot re im))) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
214.0ms	(* (log base) (log base))
247.0ms	(* (log base) (log base))

simplify2.1s

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
2	4611
1	840
0	354

prune1.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (hypot 0.0 (log base)) (/ (fma (atan2 im re) 0.0 (* (log base) (log (hypot re im)))) (hypot 0.0 (log base)))))
0.3b	(/ (fma (atan2 im re) 0.0 (* (log base) (log (hypot re im)))) (hypot 0.0 (log base)))
0.3b	(* (log base) (log (hypot re im)))
0.4b	(/ (hypot 0.0 (log base)) (/ (fma (atan2 im re) 0.0 (* (log base) (log (hypot re im)))) (hypot 0.0 (log base))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
245×	`add-sqr-sqrt`
243×	`*-un-lft-identity` `add-cube-cbrt`
60×	`associate-/r*`
34×	`add-exp-log`
23×	`div-inv`
22×	`add-cbrt-cube`
19×	`div-exp`
10×	`cbrt-undiv`
9×	`pow1` `associate-/l*`
6×	`log-prod` `associate-/r/`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `rec-exp` `clear-num` `frac-2neg` `distribute-lft-in` `1-exp`
2×	`log-pow`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `pow-flip` `inv-pow` `unswap-sqr`

Counts

4 → 335

Calls

4 calls:

17.0ms	(/ 1 (/ (hypot 0.0 (log base)) (/ (fma (atan2 im re) 0.0 (* (log base) (log (hypot re im)))) (hypot 0.0 (log base)))))
4.0ms	(/ (fma (atan2 im re) 0.0 (* (log base) (log (hypot re im)))) (hypot 0.0 (log base)))
7.0ms	(* (log base) (log (hypot re im)))
7.0ms	(/ (hypot 0.0 (log base)) (/ (fma (atan2 im re) 0.0 (* (log base) (log (hypot re im)))) (hypot 0.0 (log base))))

series1.4s

Counts

4 → 12

Calls

4 calls:

503.0ms	(/ 1 (/ (hypot 0.0 (log base)) (/ (fma (atan2 im re) 0.0 (* (log base) (log (hypot re im)))) (hypot 0.0 (log base)))))
198.0ms	(/ (fma (atan2 im re) 0.0 (* (log base) (log (hypot re im)))) (hypot 0.0 (log base)))
181.0ms	(* (log base) (log (hypot re im)))
497.0ms	(/ (hypot 0.0 (log base)) (/ (fma (atan2 im re) 0.0 (* (log base) (log (hypot re im)))) (hypot 0.0 (log base))))

simplify1.5s

Counts

347 → 347

Iterations

Iter	Nodes
done	5001
1	1388
0	516

prune2.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes543.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	19
1	19
0	16

end0.0ms

sample4.3s

Algorithm

intervals

Results

2.2s	8087×	body	80	nan
1.3s	8000×	body	80	valid