Details

sample113.0ms

Algorithm

intervals

Results

44.0ms	256×	body	80	valid
32.0ms	253×	body	80	nan

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize43.0ms

Local error

Found 3 expressions with local error:

0.3b	(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))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
38.0ms	(/ (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))

series1.1s

Counts

3 → 9

Calls

3 calls:

474.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
248.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
412.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify3.8s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.8s)

Iter	Nodes	Cost
0	99	1324
1	179	1303
2	413	1133
3	1237	1088
4	4994	1079
done	5000	1079

prune375.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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)) (hypot (log base) 0.0))
0.4b	(/ (/ (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))

rewrite34.0ms

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:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

125.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
202.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
300.0ms	(/ (/ (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))))
466.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.2s

Counts

175 → 175

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	259	6925
1	533	6630
2	1110	5576
3	2995	5382
done	5000	5253

prune964.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0b

localize32.0ms

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))
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)) (hypot (log base) 0.0)) (/ 1 (hypot (log base) 0.0)))

rewrite63.0ms

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/` `un-div-inv` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 131

Calls

4 calls:

10.0ms	(/ 1 (hypot (log base) 0.0))
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)) (hypot (log base) 0.0))
36.0ms	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (/ 1 (hypot (log base) 0.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

546.0ms	(/ 1 (hypot (log base) 0.0))
150.0ms	(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 (log base) 0.0))
274.0ms	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (/ 1 (hypot (log base) 0.0)))

simplify3.5s

Counts

143 → 143

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	186	3267
1	423	3072
2	1113	2688
3	3607	2663
done	5002	2634

prune673.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(expm1 (/ 1 (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))
0.3b	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (log1p (expm1 (/ 1 (hypot (log base) 0.0)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-r` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`expm1-log1p` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `fma-udef` `expm1-udef`

Counts

4 → 84

Calls

4 calls:

0.0ms	(expm1 (/ 1 (hypot (log base) 0.0)))
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 (log base) 0.0))
19.0ms	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (log1p (expm1 (/ 1 (hypot (log base) 0.0)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

570.0ms	(expm1 (/ 1 (hypot (log base) 0.0)))
165.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
267.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
394.0ms	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (log1p (expm1 (/ 1 (hypot (log base) 0.0)))))

simplify2.8s

Counts

96 → 96

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	152	2294
1	300	2174
2	779	1880
3	2486	1854
done	5000	1848

prune552.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

regimes415.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: done (3.0ms)

Iter	Nodes	Cost
0	16	26
1	20	24
done	20	22

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.9s	8000×	body	80	valid
1.2s	7718×	body	80	nan