Details

sample143.0ms

Algorithm

intervals

Results

68.0ms	314×	body	80	nan
34.0ms	256×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	33
2	33
1	27
0	18

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.4b	(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))))
0.6b	(* (log base) (log base))

rewrite42.0ms

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))
23.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
14.0ms	(* (log base) (log base))

series873.0ms

Counts

3 → 9

Calls

3 calls:

194.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
458.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
221.0ms	(* (log base) (log base))

simplify1.4s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1550
1	289
0	136

prune736.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

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)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
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))
0.6b	(* (log base) (log base))

rewrite72.0ms

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:

23.0ms	(/ (/ (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)))))
1.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
8.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0))
25.0ms	(* (log base) (log base))

series965.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(/ (/ (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)))))
149.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
230.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0))
270.0ms	(* (log base) (log base))

simplify1.8s

Counts

203 → 203

Iterations

Iter	Nodes
done	5002
2	2818
1	624
0	288

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 3 expressions with local error:

0.4b	(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 (pow (log base) 2)))
0.6b	(pow (log base) 2)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-exp-log`
5×	`pow1` `add-cbrt-cube`
4×	`unpow-prod-down`
3×	`expm1-log1p-u` `pow-unpow` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `pow-pow` `frac-2neg` `div-exp` `pow-exp` `log-pow` `fma-udef` `div-inv` `unpow2` `sqr-pow`

Counts

3 → 60

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 (pow (log base) 2)))
3.0ms	(pow (log base) 2)

series870.0ms

Counts

3 → 9

Calls

3 calls:

186.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
500.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2)))
184.0ms	(pow (log base) 2)

simplify1.6s

Counts

69 → 69

Iterations

Iter	Nodes
done	5002
3	3449
2	838
1	269
0	121

prune635.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (/ 1 (hypot (log base) 0.0))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
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))) (/ 1 (hypot (log base) 0.0)))
0.6b	(* (log base) (log base))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
30×	`add-exp-log`
25×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube`
19×	`pow1`
17×	`times-frac` `associate-r`
9×	`div-exp` `prod-exp`
7×	`associate-l`
6×	`log-prod` `associate-/r*` `swap-sqr` `log-pow` `sqrt-prod`
5×	`cbrt-undiv` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`rec-exp` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv` `associate-/l/`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `fma-udef` `associate-/l*`

Counts

4 → 121

Calls

4 calls:

13.0ms	(/ (* (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (/ 1 (hypot (log base) 0.0))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
20.0ms	(* (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (/ 1 (hypot (log base) 0.0)))
16.0ms	(* (log base) (log base))

series957.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(/ (* (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (/ 1 (hypot (log base) 0.0))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
144.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
201.0ms	(* (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (/ 1 (hypot (log base) 0.0)))
239.0ms	(* (log base) (log base))

simplify2.0s

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	3193
1	486
0	205

prune1.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes631.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	16

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	7990×	body	80	nan
1.7s	8000×	body	80	valid