Details

sample92.0ms

Algorithm

intervals

Results

30.0ms	256×	body	80	valid
29.0ms	248×	body	80	nan

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	18	28
1	27	21
2	33	21
done	33	21

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`fma-udef`
1×	`cbrt-undiv` `hypot-udef` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
6.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

72.0ms	(hypot re im)
148.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
281.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
505.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	111	1384
1	197	1361
2	492	1185
3	1860	1140
done	5000	1135

prune488.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
89×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r*` `div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef`
1×	`associate-/l/`

Counts

4 → 163

Calls

4 calls:

18.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
11.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

354.0ms	(/ (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
258.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
154.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
451.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.4s

Counts

175 → 175

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	259	6925
1	546	6630
2	2058	5592
done	5000	5391

prune838.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.5b	(cbrt (pow (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) 3))
0.6b	(fma (log base) (log base) (* 0.0 0.0))
0.7b	(pow (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) 3)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `unpow3` `pow-exp` `fma-udef` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 112

Calls

4 calls:

0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
6.0ms	(cbrt (pow (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) 3))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))
7.0ms	(pow (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) 3)

series1.0s

Counts

4 → 12

Calls

4 calls:

146.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
210.0ms	(cbrt (pow (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) 3))
382.0ms	(fma (log base) (log base) (* 0.0 0.0))
263.0ms	(pow (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) 3)

simplify1.5s

Counts

124 → 124

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	175	3583
1	527	3242
2	2538	2918
done	5001	2829

prune565.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2)))
0.4b	(log (exp (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2)))))
0.5b	(exp (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2))))
0.6b	(pow (log base) 2)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

5.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2)))
9.0ms	(log (exp (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2)))))
7.0ms	(exp (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2))))
3.0ms	(pow (log base) 2)

series731.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2)))
167.0ms	(log (exp (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2)))))
213.0ms	(exp (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma 0.0 0.0 (pow (log base) 2))))
170.0ms	(pow (log base) 2)

simplify1.6s

Counts

112 → 112

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	158	2475
1	293	2361
2	808	2110
3	2993	2098
done	5001	2090

prune654.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes362.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	30
1	20	30
done	20	30

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
1.2s	7721×	body	80	nan