Details

sample168.0ms

Algorithm

intervals

Results

65.0ms	256×	body	80	valid
45.0ms	241×	body	80	nan

simplify60.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
2	32
1	27
0	18

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize434.0ms

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))))
0.5b	(* (log base) (log base))

rewrite29.0ms

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` `insert-posit16` `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 → 80

Calls

3 calls:

1.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
7.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
16.0ms	(* (log base) (log base))

series1.2s

Counts

3 → 9

Calls

3 calls:

289.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
679.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
277.0ms	(* (log base) (log base))

simplify4.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
3	1899
2	704
1	291
0	139

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize95.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.3b	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
0.5b	(* (log base) (log base))
0.5b	(* (log base) (log base))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
172×	`add-sqr-sqrt` `*-un-lft-identity`
168×	`add-cube-cbrt`
144×	`sqrt-prod`
30×	`pow1`
25×	`associate-/l*`
15×	`add-cbrt-cube` `add-exp-log`
12×	`log-prod` `associate-/r*` `swap-sqr` `log-pow`
9×	`div-inv`
8×	`associate-r` `associate-l`
6×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `clear-num` `frac-2neg` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 298

Calls

4 calls:

37.0ms	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
9.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
14.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))

series2.1s

Counts

4 → 12

Calls

4 calls:

800.0ms	(/ (/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base))))) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
763.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
249.0ms	(* (log base) (log base))
263.0ms	(* (log base) (log base))

simplify3.8s

Counts

310 → 310

Iterations

Iter	Nodes
done	5001
2	1722
1	737
0	329

prune4.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0b

localize174.0ms

Local error

Found 4 expressions with local error:

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

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
28×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`log-prod` `swap-sqr` `log-pow`
12×	`associate-r` `associate-l`
10×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `pow-plus` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`pow3`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 130

Calls

4 calls:

26.0ms	(* (log base) (log base))
15.0ms	(* (log base) (log base))
14.0ms	(* (log base) (log base))
174.0ms	(cbrt (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))))

series1.0s

Counts

4 → 12

Calls

4 calls:

258.0ms	(* (log base) (log base))
263.0ms	(* (log base) (log base))
251.0ms	(* (log base) (log base))
257.0ms	(cbrt (* (* (* (log base) (log base)) (log base)) (* (* (log base) (log base)) (log base))))

simplify6.0s

Counts

142 → 142

Iterations

Iter	Nodes
done	5000
4	1887
3	733
2	369
1	149
0	69

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (hypot (log base) 0.0) (hypot (log base) 0.0)))
0.3b	(* (log (hypot re im)) (log base))
0.4b	(* (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (/ 1 (* (hypot (log base) 0.0) (hypot (log base) 0.0))))
0.5b	(* (hypot (log base) 0.0) (hypot (log base) 0.0))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
26×	`add-sqr-sqrt`
25×	`pow1`
22×	`add-cbrt-cube`
18×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`prod-exp`
14×	`associate-r`
10×	`associate-l`
8×	`times-frac` `div-exp`
7×	`cbrt-unprod`
6×	`log-prod` `pow-flip`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `rec-exp` `hypot-udef` `1-exp` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `-commutative` `associate-/l`
2×	`pow2` `pow-plus` `pow-sqr` `log-pow` `pow-prod-up` `div-inv`
1×	`clear-num` `associate-/r` `rem-square-sqrt` `frac-2neg` `sqrt-unprod` `associate-r/` `un-div-inv` `inv-pow`

Counts

4 → 131

Calls

4 calls:

17.0ms	(/ 1 (* (hypot (log base) 0.0) (hypot (log base) 0.0)))
24.0ms	(* (log (hypot re im)) (log base))
40.0ms	(* (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (/ 1 (* (hypot (log base) 0.0) (hypot (log base) 0.0))))
11.0ms	(* (hypot (log base) 0.0) (hypot (log base) 0.0))

series2.1s

Counts

4 → 12

Calls

4 calls:

759.0ms	(/ 1 (* (hypot (log base) 0.0) (hypot (log base) 0.0)))
216.0ms	(* (log (hypot re im)) (log base))
439.0ms	(* (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (/ 1 (* (hypot (log base) 0.0) (hypot (log base) 0.0))))
644.0ms	(* (hypot (log base) 0.0) (hypot (log base) 0.0))

simplify9.4s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
3	4926
2	1280
1	457
0	198

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes1.2s

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	14

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
1.7s	7906×	body	80	nan