Details

sample91.0ms

Algorithm

intervals

Results

31.0ms	254×	body	80	nan
29.0ms	256×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	33
2	33
1	27
0	18

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize49.0ms

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))

rewrite18.0ms

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:

5.0ms	(/ (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))
9.0ms	(* (log base) (log base))

series766.0ms

Counts

3 → 9

Calls

3 calls:

385.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
184.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
197.0ms	(* (log base) (log base))

simplify1.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1539
1	289
0	136

prune633.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0))
0.4b	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
0.4b	(/ (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.6b	(* (log base) (log base))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
97×	`add-sqr-sqrt` `*-un-lft-identity`
95×	`add-cube-cbrt`
42×	`sqrt-prod`
17×	`pow1`
16×	`associate-/l*`
13×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`clear-num` `frac-2neg`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 191

Calls

4 calls:

6.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0))
0.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
15.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
11.0ms	(* (log base) (log base))

series884.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0))
144.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
320.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
208.0ms	(* (log base) (log base))

simplify1.8s

Counts

203 → 203

Iterations

Iter	Nodes
done	5001
2	2811
1	621
0	288

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 1) (/ (hypot (log base) 0.0) (/ (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))
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)) (hypot (log base) 0.0)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

1985×	`times-frac`
859×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
108×	`div-inv`
71×	`add-exp-log`
60×	`associate-/r*`
58×	`div-exp`
32×	`add-cbrt-cube`
19×	`cbrt-undiv` `associate-/l*`
16×	`associate-/r/`
15×	`1-exp`
6×	`rec-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`fma-udef` `associate-/l/`

Counts

4 → 781

Calls

4 calls:

31.0ms	(/ (/ 1 1) (/ (hypot (log base) 0.0) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))))
4.0ms	(/ (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))
10.0ms	(/ (hypot (log base) 0.0) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

488.0ms	(/ (/ 1 1) (/ (hypot (log base) 0.0) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))))
210.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
113.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
546.0ms	(/ (hypot (log base) 0.0) (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

simplify583.0ms

Counts

793 → 793

Iterations

Iter	Nodes
done	5000
0	1224

prune4.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
0.4b	(/ (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0)) (sqrt (fma 0.0 0.0 (+ (* (* 2 (log (cbrt base))) (log base)) (* (log base) (log (cbrt base)))))))
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

0.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
11.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0)) (sqrt (fma 0.0 0.0 (+ (* (* 2 (log (cbrt base))) (log base)) (* (log base) (log (cbrt base)))))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.2s

Counts

4 → 12

Calls

4 calls:

143.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
575.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0)) (sqrt (fma 0.0 0.0 (+ (* (* 2 (log (cbrt base))) (log base)) (* (log base) (log (cbrt base)))))))
254.0ms	(cbrt base)
238.0ms	(cbrt base)

simplify883.0ms

Counts

162 → 162

Iterations

Iter	Nodes
done	5000
2	2336
1	605
0	275

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes476.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.0s	7946×	body	80	nan