Details

sample141.0ms

Algorithm

intervals

Results

53.0ms	307×	body	80	nan
49.0ms	256×	body	80	valid

simplify23.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	33
2	33
1	27
0	18

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize48.0ms

Local error

Found 3 expressions with local error:

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))))
0.5b	(* (log base) (log base))

rewrite28.0ms

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:

1.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
8.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
16.0ms	(* (log base) (log base))

series868.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
419.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
269.0ms	(* (log base) (log base))

simplify1.7s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1550
1	289
0	136

prune693.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))

rewrite66.0ms

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))
15.0ms	(/ (/ (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))
19.0ms	(* (log base) (log base))

series1.1s

Counts

4 → 12

Calls

4 calls:

191.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
488.0ms	(/ (/ (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)))))
232.0ms	(* (log base) (log base))
227.0ms	(* (log base) (log base))

simplify2.2s

Counts

275 → 275

Iterations

Iter	Nodes
done	5001
2	4207
1	762
0	322

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize48.0ms

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

rewrite66.0ms

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))))
12.0ms	(/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0))
7.0ms	(/ (hypot (log base) 0.0) (/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0)))
13.0ms	(* (log (hypot re im)) (log base))

series1.5s

Counts

4 → 12

Calls

4 calls:

497.0ms	(/ 1 (/ (hypot (log base) 0.0) (/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0))))
226.0ms	(/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0))
590.0ms	(/ (hypot (log base) 0.0) (/ (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (hypot (log base) 0.0)))
143.0ms	(* (log (hypot re im)) (log base))

simplify1.5s

Counts

347 → 347

Iterations

Iter	Nodes
done	5001
1	1385
0	516

prune2.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 3 expressions with local error:

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))))
0.5b	(* (log base) (log base))

rewrite19.0ms

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:

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))))
13.0ms	(* (log base) (log base))

series762.0ms

Counts

3 → 9

Calls

3 calls:

185.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
394.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
182.0ms	(* (log base) (log base))

simplify1.4s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1550
1	289
0	136

prune806.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes518.0ms

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	18
1	18
0	15

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.2s	7995×	body	80	nan