Details

sample80.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
26.0ms	254×	body	80	nan

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	33
2	33
1	27
0	18

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 3 expressions with local error:

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))
0.6b	(* (log base) (log base))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`pow1`
9×	`times-frac`
7×	`add-cbrt-cube` `add-exp-log`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`associate-r` `associate-l`
3×	`distribute-rgt-in` `expm1-log1p-u` `associate-/r` `distribute-lft-in` `log1p-expm1-u` `associate-/l` `add-log-exp`
1×	`pow2` `cbrt-undiv` `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

3 → 77

Calls

3 calls:

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

series811.0ms

Counts

3 → 9

Calls

3 calls:

421.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
192.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
198.0ms	(* (log base) (log base))

simplify1.4s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1539
1	289
0	136

prune708.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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)))))
10.0ms	(* (log base) (log base))
8.0ms	(* (log base) (log base))

series882.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
354.0ms	(/ (/ (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)))))
187.0ms	(* (log base) (log base))
169.0ms	(* (log base) (log base))

simplify2.3s

Counts

275 → 275

Iterations

Iter	Nodes
done	5001
2	4207
1	762
0	322

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

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:

18.0ms	(/ 1 (/ (hypot (log base) 0.0) (/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0))))
4.0ms	(/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0))
8.0ms	(* (log (hypot re im)) (log base))
21.0ms	(/ (hypot (log base) 0.0) (/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

541.0ms	(/ 1 (/ (hypot (log base) 0.0) (/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0))))
218.0ms	(/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0))
133.0ms	(* (log (hypot re im)) (log base))
594.0ms	(/ (hypot (log base) 0.0) (/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0)))

simplify1.9s

Counts

347 → 347

Iterations

Iter	Nodes
done	5000
1	1388
0	516

prune3.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (log base) (log (hypot re im)))
0.4b	(/ (/ (+ (* (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))

rewrite86.0ms

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:

8.0ms	(* (log base) (log (hypot re im)))
45.0ms	(/ (/ (+ (* (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))

series1.3s

Counts

4 → 12

Calls

4 calls:

217.0ms	(* (log base) (log (hypot re im)))
523.0ms	(/ (/ (+ (* (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)))))
267.0ms	(* (log base) (log base))
300.0ms	(* (log base) (log base))

simplify2.8s

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
2	4611
1	840
0	354

prune2.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes630.0ms

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

sample4.2s

Algorithm

intervals

Results

1.9s	7946×	body	80	nan
1.5s	8000×	body	80	valid