Details

sample58.0ms

Algorithm

intervals

Results

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

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	27	28
2	44	28
3	56	28
4	74	28
5	80	28
done	80	28

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.3b	(* (atan2 im re) (log base))
0.5b	(* (log base) (log base))
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod`
10×	`add-exp-log` `add-cbrt-cube`
9×	`times-frac`
8×	`associate-r`
7×	`associate-l` `log-pow`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `sqrt-prod` `associate-/l`
2×	`flip3-+` `sqrt-div` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 108

Calls

4 calls:

12.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms	(* (atan2 im re) (log base))
4.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
33.0ms	(* (atan2 im re) (log base))
155.0ms	(* (log base) (log base))
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify581.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (150.0ms)

Iter	Nodes	Cost
0	194	2236
1	446	2040
2	1582	1850
done	5001	1850

prune469.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

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` `frac-2neg` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 63

Calls

1 calls:

4.0ms

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

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

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

simplify1.9s

Counts

66 → 66

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	106	887
1	188	841
2	471	815
3	1114	809
4	2538	807
done	5000	804

prune160.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 66

Calls

2 calls:

2.0ms	(/ -1 (log base))
8.0ms	(* (atan2 im re) (/ -1 (log base)))

series207.0ms

Counts

2 → 6

Calls

2 calls:

162.0ms	(/ -1 (log base))
45.0ms	(* (atan2 im re) (/ -1 (log base)))

simplify1.6s

Counts

72 → 72

Iterations

Useful iterations: 3 (326.0ms)

Iter	Nodes	Cost
0	99	713
1	211	644
2	748	586
3	2895	578
done	5001	578

prune193.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite31.0ms

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×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`neg-sub0` `pow-flip` `div-sub` `distribute-frac-neg` `associate-/r/` `inv-pow`

Counts

2 → 249

Calls

2 calls:

5.0ms	(/ (- (log base)) (atan2 im re))
12.0ms	(/ 1 (/ (- (log base)) (atan2 im re)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- (log base)) (atan2 im re))
60.0ms	(/ 1 (/ (- (log base)) (atan2 im re)))

simplify290.0ms

Iterations

Useful iterations: 1 (70.0ms)

Iter	Nodes	Cost
0	303	4424
1	701	3905