Details

sample97.0ms

Algorithm

intervals

Results

34.0ms	256×	body	80	valid
31.0ms	224×	body	80	nan

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	18	28
1	27	21
2	33	21
done	33	21

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`fma-udef`
1×	`cbrt-undiv` `hypot-udef` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

1.0ms	(hypot re im)
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
6.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series923.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(hypot re im)
129.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
259.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
463.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.4s

Counts

71 → 71

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	111	1384
1	196	1361
2	433	1185
3	1261	1140
done	5000	1131

prune580.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
89×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*` `div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef`
1×	`associate-/l/`

Counts

4 → 163

Calls

4 calls:

5.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
32.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

257.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
182.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
383.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
451.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.3s

Counts

175 → 175

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	259	6925
1	533	6630
2	1110	5576
3	2996	5382
done	5002	5253

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

12.0ms	(/ 1 (hypot (log base) 0.0))
5.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
25.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base))))

series1.6s

Counts

4 → 12

Calls

4 calls:

574.0ms	(/ 1 (hypot (log base) 0.0))
226.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))
159.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
643.0ms	(* (/ 1 (hypot (log base) 0.0)) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base))))

simplify3.4s

Counts

142 → 142

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	197	3303
1	437	3105
2	1252	2729
3	4166	2723
done	5000	2721

prune881.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.3b	(/ (* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (hypot (log base) 0.0))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
0.3b	(* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (hypot (log base) 0.0)))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
23×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
17×	`*-un-lft-identity` `times-frac`
16×	`add-cube-cbrt`
13×	`associate-r`
9×	`div-exp`
8×	`prod-exp`
6×	`pow1` `associate-/r*` `sqrt-prod`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`rec-exp` `1-exp` `associate-*r/` `un-div-inv` `fma-udef` `div-inv` `associate-/l/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
19.0ms	(/ (* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (hypot (log base) 0.0))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
18.0ms	(* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (hypot (log base) 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

125.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
402.0ms	(/ (* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (hypot (log base) 0.0))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
257.0ms	(* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (hypot (log base) 0.0)))
783.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify3.0s

Counts

105 → 105

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	178	2645
1	384	2407
2	1013	1830
3	3820	1780
done	5000	1779

prune566.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes310.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	24
1	20	24
done	20	24

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.2s	7907×	body	80	nan