Details

sample74.0ms

Algorithm

intervals

Results

25.0ms	289×	body	80	nan
21.0ms	256×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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:

0.0ms	(hypot re im)
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
9.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series755.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(hypot re im)
168.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
241.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
294.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: done (1.2s)

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

prune489.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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:

13.0ms	(/ (/ (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))))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
14.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

392.0ms	(/ (/ (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))))
118.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
235.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
433.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.5s

Counts

175 → 175

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	259	6925
1	533	6630
2	1104	5576
3	2985	5382
done	5000	5253

prune918.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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:

5.0ms	(/ 1 (hypot 0.0 (log base)))
27.0ms	(* (/ 1 (hypot 0.0 (log base))) (/ (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))
5.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))

series1.3s

Counts

4 → 12

Calls

4 calls:

507.0ms	(/ 1 (hypot 0.0 (log base)))
444.0ms	(* (/ 1 (hypot 0.0 (log base))) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base))))
113.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
228.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))

simplify3.2s

Counts

142 → 142

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	185	3303
1	419	3105
2	1221	2729
3	4139	2714
done	5001	2675

prune616.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.4b	(/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

735×	`times-frac`
347×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
135×	`sqrt-prod`
47×	`associate-/l*`
30×	`div-inv`
25×	`add-exp-log`
15×	`div-exp` `add-cbrt-cube`
9×	`associate-/r*`
7×	`cbrt-undiv` `associate-/r/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef`
1×	`associate-/l/`

Counts

4 → 386

Calls

4 calls:

40.0ms	(/ (/ 1 (/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
5.0ms	(/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

619.0ms	(/ (/ 1 (/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
195.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
589.0ms	(/ (hypot (log base) 0.0) (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)))
742.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.1s

Counts

398 → 398

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	634	20577
1	1403	18839
2	2381	15550
done	5000	15001

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes361.0ms

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	15	24
1	19	24
done	19	24

end0.0ms

sample2.4s

Algorithm

intervals

Results

845.0ms	8043×	body	80	nan
813.0ms	8000×	body	80	valid