Details

sample122.0ms

Algorithm

intervals

Results

43.0ms	273×	body	80	nan
36.0ms	256×	body	80	valid

simplify39.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	33
2	33
1	27
0	18

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 3 expressions with local error:

0.3b	(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))

rewrite15.0ms

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:

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 (* (log base) (log base))))
8.0ms	(* (log base) (log base))

series831.0ms

Counts

3 → 9

Calls

3 calls:

202.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
422.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
207.0ms	(* (log base) (log base))

simplify1.6s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1550
1	289
0	136

prune710.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

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

rewrite55.0ms

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:

18.0ms	(/ (/ (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)))))
8.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0))
1.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
16.0ms	(* (log base) (log base))

series944.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(/ (/ (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)))))
236.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0))
117.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
220.0ms	(* (log base) (log base))

simplify1.9s

Counts

203 → 203

Iterations

Iter	Nodes
done	5000
2	2826
1	624
0	288

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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

rewrite70.0ms

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×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 131

Calls

4 calls:

8.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0))
8.0ms	(/ 1 (hypot (log base) 0.0))
46.0ms	(* (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0)) (/ 1 (hypot (log base) 0.0)))
1.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))

series1.1s

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0))
490.0ms	(/ 1 (hypot (log base) 0.0))
216.0ms	(* (/ (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (hypot (log base) 0.0)) (/ 1 (hypot (log base) 0.0)))
137.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))

simplify2.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	2971
1	463
0	186

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

155×	`times-frac`
103×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
90×	`add-cube-cbrt`
43×	`associate-r`
32×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/l*`
14×	`div-exp`
11×	`div-inv`
10×	`pow1`
7×	`cbrt-undiv`
6×	`associate-/r*`
5×	`prod-exp` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `pow-flip` `inv-pow` `pow-div`
1×	`pow-prod-down` `associate-r/` `-commutative` `fma-udef` `associate-/l/`

Counts

4 → 190

Calls

4 calls:

12.0ms	(/ (/ 1 (hypot (log base) 0.0)) (hypot (log base) 0.0))
4.0ms	(/ 1 (hypot (log base) 0.0))
0.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
40.0ms	(* (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (/ (/ 1 (hypot (log base) 0.0)) (hypot (log base) 0.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

639.0ms	(/ (/ 1 (hypot (log base) 0.0)) (hypot (log base) 0.0))
523.0ms	(/ 1 (hypot (log base) 0.0))
170.0ms	(fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re)))
266.0ms	(* (fma (log (hypot re im)) (log base) (* 0.0 (atan2 im re))) (/ (/ 1 (hypot (log base) 0.0)) (hypot (log base) 0.0)))

simplify1.6s

Counts

202 → 202

Iterations

Iter	Nodes
done	5000
2	3341
1	649
0	264

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes558.0ms

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	15

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.8s	8000×	body	80	valid
1.5s	8160×	body	80	nan