Details

sample97.0ms

Algorithm

intervals

Results

39.0ms	232×	body	80	nan
29.0ms	256×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize36.0ms

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

rewrite15.0ms

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:

1.0ms	(hypot re im)
10.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 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))

series1.3s

Counts

4 → 12

Calls

4 calls:

63.0ms	(hypot re im)
236.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
185.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
838.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	111	1384
1	197	1361
2	492	1185
3	1852	1140
done	5001	1135

prune616.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

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

rewrite47.0ms

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:

8.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
30.0ms	(/ (/ (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))))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

245.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
337.0ms	(/ (/ (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))))
148.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
443.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.3s

Counts

175 → 175

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	259	6925
1	546	6630
2	2082	5592
done	5001	5387

prune880.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (log (exp (/ (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))))
0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.5b	(fma (log base) (log base) (* 0.0 0.0))
5.8b	(exp (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
104×	`exp-prod`
103×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
98×	`log-pow`
54×	`sqrt-prod`
17×	`associate-/l*`
11×	`pow1`
9×	`div-inv`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `rem-exp-log`

Counts

4 → 182

Calls

4 calls:

42.0ms	(/ (log (exp (/ (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))))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))
7.0ms	(exp (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

series983.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(/ (log (exp (/ (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))))
138.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
386.0ms	(fma (log base) (log base) (* 0.0 0.0))
164.0ms	(exp (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)))

simplify1.2s

Counts

194 → 194

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	310	8252
1	521	7582
2	2334	6452
done	5000	6221

prune997.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

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

Counts

4 → 131

Calls

4 calls:

5.0ms	(/ 1 (hypot (log base) 0.0))
16.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
49.0ms	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (/ 1 (hypot (log base) 0.0)))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

408.0ms	(/ 1 (hypot (log base) 0.0))
203.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
308.0ms	(* (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0)) (/ 1 (hypot (log base) 0.0)))
170.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))

simplify2.0s

Counts

143 → 143

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	186	3267
1	463	3084
2	2964	2702
done	5001	2701

prune661.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes271.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	19	24
done	19	24

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.2s	8096×	body	80	nan