Details

sample72.0ms

Algorithm

intervals

Results

28.0ms	305×	body	80	nan
23.0ms	256×	body	80	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune44.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

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

series866.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(hypot re im)
159.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
249.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
385.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify1.4s

Counts

71 → 71

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	111	1384
1	196	1361
2	433	1185
3	1261	1140
done	5000	1131

prune585.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

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

rewrite45.0ms

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:

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))
25.0ms	(/ (/ (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))))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

258.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot (log base) 0.0))
152.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
444.0ms	(/ (/ (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))))
499.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify2.6s

Counts

175 → 175

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	259	6925
1	533	6630
2	1110	5576
3	2996	5382
done	5002	5253

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac` `add-cbrt-cube`
9×	`associate-/r*`
8×	`div-exp`
6×	`sqrt-prod`
5×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `prod-exp` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `1-exp` `clear-num` `cbrt-unprod` `fma-udef` `div-inv`
1×	`associate-*r/` `associate-/l/`

Counts

4 → 83

Calls

4 calls:

10.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))
1.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
30.0ms	(/ (* 1 (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
1.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

231.0ms	(/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))
150.0ms	(fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0))
394.0ms	(/ (* 1 (/ (fma (log (hypot re im)) (log base) (* (atan2 im re) 0.0)) (hypot 0.0 (log base)))) (sqrt (fma (log base) (log base) (* 0.0 0.0))))
489.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify3.4s

Counts

95 → 95

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	168	2489
1	328	2327
2	924	1841
3	2926	1769
done	5001	1768

prune680.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
0.3b	(* (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
0.4b	(* (log (hypot re im)) (log base))
0.5b	(pow (log base) 2)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`add-exp-log` `times-frac`
17×	`associate-r`
13×	`pow1` `add-cbrt-cube`
7×	`associate-l`
6×	`log-prod`
5×	`prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in` `associate-/r` `log-pow` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`pow-to-exp` `pow-flip` `pow-pow` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `un-div-inv` `unpow2` `inv-pow` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

19.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
31.0ms	(* (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
21.0ms	(* (log (hypot re im)) (log base))
7.0ms	(pow (log base) 2)

series872.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(/ 1 (fma 0.0 0.0 (pow (log base) 2)))
205.0ms	(* (fma (atan2 im re) 0.0 (* (log (hypot re im)) (log base))) (/ 1 (fma 0.0 0.0 (pow (log base) 2))))
145.0ms	(* (log (hypot re im)) (log base))
180.0ms	(pow (log base) 2)

simplify3.8s

Counts

132 → 132

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	201	2110
1	392	1926
2	996	1642
3	3542	1627
done	5000	1624

prune633.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

Details

sample72.0ms

simplify17.0ms

prune44.0ms

localize20.0ms

rewrite8.0ms

series866.0ms

simplify1.4s

prune585.0ms

localize47.0ms

rewrite45.0ms

series1.4s

simplify2.6s

prune1.0s

localize50.0ms

rewrite46.0ms

series1.3s

simplify3.4s

prune680.0ms

localize43.0ms

rewrite86.0ms

series872.0ms

simplify3.8s

prune633.0ms

regimes15.0ms