Details

sample59.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
17.0ms	252×	body	80	nan

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

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))

rewrite4.0ms

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)
2.0ms	(/ (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 (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series594.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(hypot re im)
154.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
113.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
280.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.3s

Counts

71 → 71

Iterations

Useful iterations: 4 (553.0ms)

Iter	Nodes	Cost
0	111	1384
1	199	1361
2	474	1185
3	1293	1140
4	4837	1131
done	5000	1131

prune341.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))))
0.4b	(/ (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))
0.5b	(fma (log base) (log base) (* 0.0 0.0))

rewrite20.0ms

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:

7.0ms	(/ (/ (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))))
5.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 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))

series787.0ms

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)) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
154.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
114.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
274.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.4s

Counts

175 → 175

Iterations

Useful iterations: 3 (962.0ms)

Iter	Nodes	Cost
0	259	6925
1	542	6658
2	1668	5576
3	4675	5382
done	5000	5382

prune616.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.4b	(* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.4b	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
0.5b	(pow (log base) 2)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`times-frac`
18×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
9×	`pow1`
4×	`expm1-log1p-u` `unpow-prod-down` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `un-div-inv` `-commutative` `fma-udef` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

2.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
8.0ms	(* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
2.0ms	(pow (log base) 2)

series626.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
147.0ms	(* (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
110.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
151.0ms	(pow (log base) 2)

simplify2.0s

Counts

114 → 114

Iterations

Useful iterations: 3 (513.0ms)

Iter	Nodes	Cost
0	163	1963
1	350	1816
2	1066	1518
3	3568	1510
done	5001	1510

prune382.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (pow (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 3) (pow (hypot (log base) 0.0) 6))
0.6b	(cbrt (/ (pow (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 3) (pow (hypot (log base) 0.0) 6)))
0.7b	(pow (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 3)
1.2b	(pow (hypot (log base) 0.0) 6)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
126×	`unpow-prod-down`
105×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
88×	`cbrt-prod`
48×	`cube-prod`
42×	`sqr-pow`
18×	`add-exp-log`
16×	`cube-mult` `unpow3`
12×	`associate-/l*`
9×	`div-exp`
8×	`pow-to-exp` `pow-exp`
7×	`associate-/r*` `add-cbrt-cube`
6×	`pow1` `pow-unpow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow` `div-inv`
1×	`cbrt-undiv` `cbrt-div` `hypot-udef` `frac-2neg` `pow1/3` `clear-num` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 269

Calls

4 calls:

8.0ms	(/ (pow (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 3) (pow (hypot (log base) 0.0) 6))
7.0ms	(cbrt (/ (pow (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 3) (pow (hypot (log base) 0.0) 6)))
1.0ms	(pow (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 3)
1.0ms	(pow (hypot (log base) 0.0) 6)

series1.0s

Counts

4 → 12

Calls

4 calls:

249.0ms	(/ (pow (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 3) (pow (hypot (log base) 0.0) 6))
191.0ms	(cbrt (/ (pow (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 3) (pow (hypot (log base) 0.0) 6)))
159.0ms	(pow (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) 3)
416.0ms	(pow (hypot (log base) 0.0) 6)

simplify76.0ms

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	343	10585