Details

sample116.0ms

Algorithm

intervals

Results

47.0ms	263×	body	80	nan
36.0ms	256×	body	80	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
2	32
1	27
0	18

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize51.0ms

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))

rewrite23.0ms

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))
6.0ms	(/ (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))

series909.0ms

Counts

3 → 9

Calls

3 calls:

240.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
446.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (* (log base) (log base))))
222.0ms	(* (log base) (log base))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
3	1855
2	707
1	288
0	136

prune517.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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:

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

series960.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
428.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (sqrt (fma 0.0 0.0 (* (log base) (log base)))))
187.0ms	(* (log base) (log base))
180.0ms	(* (log base) (log base))

simplify1.8s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	1984
2	787
1	309
0	153

prune894.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`cbrt-prod` `log-prod`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `pow1/3` `log-pow` `associate-/l`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

11.0ms	(* (log (cbrt base)) (log base))
5.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (+ (* (log (cbrt base)) (+ (log base) (log base))) (* (log (cbrt base)) (log base)))))
1.0ms	(cbrt base)
1.0ms	(cbrt base)

series1.5s

Counts

4 → 12

Calls

4 calls:

468.0ms	(* (log (cbrt base)) (log base))
500.0ms	(/ (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (+ (* (log (cbrt base)) (+ (log base) (log base))) (* (log (cbrt base)) (log base)))))
239.0ms	(cbrt base)
271.0ms	(cbrt base)

simplify2.0s

Counts

96 → 96

Iterations

Iter	Nodes
done	5009
3	3023
2	865
1	313
0	157

prune726.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

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

Counts

4 → 155

Calls

4 calls:

9.0ms	(/ 1 (/ (fma 0.0 0.0 (* (log base) (log base))) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))
0.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
4.0ms	(/ (fma 0.0 0.0 (* (log base) (log base))) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
9.0ms	(* (log base) (log base))

series1.2s

Counts

4 → 12

Calls

4 calls:

402.0ms	(/ 1 (/ (fma 0.0 0.0 (* (log base) (log base))) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))))
182.0ms	(fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0))
461.0ms	(/ (fma 0.0 0.0 (* (log base) (log base))) (fma (log base) (log (hypot re im)) (* (atan2 im re) 0.0)))
205.0ms	(* (log base) (log base))

simplify2.1s

Counts

167 → 167

Iterations

Iter	Nodes
done	5001
3	3681
2	1285
1	545
0	236

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes438.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	15

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.1s	7937×	body	80	nan