Details

sample59.0ms

Algorithm

intervals

Results

22.0ms	252×	body	80	nan
18.0ms	256×	body	80	valid

simplify54.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	28
1	31	22
2	52	22
3	68	22
4	88	22
5	100	22
6	104	22
done	104	22

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 4 expressions with local error:

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

series426.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(hypot re im)
72.0ms	(/ (fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im))))) (fma (log base) (log base) (* 0.0 0.0)))
31.0ms	(fma (atan2 im re) (log base) (- (* 0.0 (log (hypot re im)))))
276.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify545.0ms

Counts

71 → 71

Iterations

Useful iterations: done (543.0ms)

Iter	Nodes	Cost
0	105	1432
1	189	1415
2	454	1233
3	1308	1180
done	5000	1176

prune344.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ (atan2 im re) (- (log base)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/r*`
9×	`pow1`
8×	`log-pow`
4×	`neg-mul-1`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`cbrt-undiv` `expm1-log1p-u` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 65

Calls

1 calls:

4.0ms

(/ (atan2 im re) (- (log base)))

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

(/ (atan2 im re) (- (log base)))

simplify1.6s

Counts

68 → 68

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	108	903
1	190	861
2	470	835
3	1112	829
4	2520	827
done	5000	824

prune188.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ -1 (log base))
0.3b	(* (atan2 im re) (/ -1 (log base)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
11×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow`
4×	`associate-/r*`
3×	`associate-l` `associate-/l*`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 70

Calls

2 calls:

2.0ms	(/ -1 (log base))
9.0ms	(* (atan2 im re) (/ -1 (log base)))

series216.0ms

Counts

2 → 6

Calls

2 calls:

172.0ms	(/ -1 (log base))
44.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify1.8s

Counts

76 → 76

Iterations

Useful iterations: 3 (320.0ms)

Iter	Nodes	Cost
0	103	741
1	213	670
2	748	612
3	2915	604
done	5000	604

prune225.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (- (log base)) (atan2 im re))
0.4b	(/ 1 (/ (- (log base)) (atan2 im re)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

300×	`times-frac`
156×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
64×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
43×	`associate-/r*`
35×	`pow1`
32×	`log-pow`
16×	`neg-mul-1`
15×	`add-exp-log` `associate-/l*`
9×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `associate-/r/` `inv-pow`

Counts

2 → 253

Calls

2 calls:

6.0ms	(/ (- (log base)) (atan2 im re))
12.0ms	(/ 1 (/ (- (log base)) (atan2 im re)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- (log base)) (atan2 im re))
56.0ms	(/ 1 (/ (- (log base)) (atan2 im re)))

simplify294.0ms

Iterations

Useful iterations: 1 (67.0ms)

Iter	Nodes	Cost
0	307	4460
1	705	3941