Details

sample82.0ms

Algorithm

intervals

Results

34.0ms	256×	body	80	valid
24.0ms	252×	body	80	nan

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	33
2	33
1	27
0	18

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
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))
0.5b	(* (log base) (log base))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
17×	`pow1`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`log-prod` `swap-sqr` `log-pow`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `associate-/l`
1×	`pow2` `cbrt-undiv` `hypot-udef` `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

4 → 87

Calls

4 calls:

0.0ms	(hypot re im)
4.0ms	(/ (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))
20.0ms	(* (log base) (log base))

series842.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot re im)
369.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
195.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
228.0ms	(* (log base) (log base))

simplify1.5s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1567
1	306
0	148

prune809.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`pow1`
18×	`times-frac`
12×	`log-prod` `swap-sqr` `log-pow` `sqrt-prod`
10×	`add-cbrt-cube` `add-exp-log`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `associate-/r*` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 127

Calls

4 calls:

5.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
8.0ms	(* (log base) (log base))
13.0ms	(* (log base) (log base))

series1.0s

Counts

4 → 12

Calls

4 calls:

383.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
180.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
245.0ms	(* (log base) (log base))
225.0ms	(* (log base) (log base))

simplify1.5s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
2	1582
1	310
0	153

prune978.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt base) (cbrt base))
0.6b	(cbrt base)
0.6b	(cbrt base)
0.6b	(cbrt base)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

13.0ms	(* (cbrt base) (cbrt base))
1.0ms	(cbrt base)
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.3s

Counts

4 → 12

Calls

4 calls:

594.0ms	(* (cbrt base) (cbrt base))
232.0ms	(cbrt base)
241.0ms	(cbrt base)
255.0ms	(cbrt base)

simplify1.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	725
1	142
0	65

prune753.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
0.5b	(* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
0.5b	(* (log base) (log base))
0.6b	(cbrt (* (* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`swap-sqr`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-r` `associate-l`
6×	`log-prod` `log-pow`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 89

Calls

4 calls:

0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
6.0ms	(* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
8.0ms	(* (log base) (log base))
11.0ms	(cbrt (* (* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))

series795.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
291.0ms	(* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
169.0ms	(* (log base) (log base))
152.0ms	(cbrt (* (* (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))

simplify1.3s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1618
1	265
0	121

prune728.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0b

regimes672.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	7931×	body	80	nan
1.2s	8000×	body	80	valid