Details

sample110.0ms

Algorithm

intervals

Results

42.0ms	273×	body	80	nan
37.0ms	256×	body	80	valid

simplify116.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	18	724
1	31	594
2	51	594
3	67	594
4	87	594
5	91	594
done	91	594

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`log-prod`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `associate-l` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `hypot-udef` `clear-num` `frac-2neg` `flip3--` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

0.0ms	(hypot re im)
31.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
12.0ms	(* (atan2 im re) (log base))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series563.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(hypot re im)
76.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (fma (log base) (log base) (* 0.0 0.0)))
30.0ms	(* (atan2 im re) (log base))
402.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify3.9s

Counts

91 → 91

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	153	42856
1	329	41488
2	939	40154
3	3189	39839
done	5074	39814

prune836.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`associate-/r*` `log-pow`
3×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
1×	`expm1-log1p-u` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

4.0ms

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

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

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

simplify5.4s

Counts

36 → 36

Iterations

Useful iterations: 5 (3.9s)

Iter	Nodes	Cost
0	64	14350
1	110	13912
2	273	13832
3	668	13722
4	1906	13681
5	4930	13601
done	5000	13601

prune272.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 78

Calls

2 calls:

7.0ms	(/ 1 (log base))
22.0ms	(* (atan2 im re) (/ 1 (log base)))

series259.0ms

Counts

2 → 6

Calls

2 calls:

208.0ms	(/ 1 (log base))
51.0ms	(* (atan2 im re) (/ 1 (log base)))

simplify4.6s

Counts

84 → 84

Iterations

Useful iterations: done (4.6s)

Iter	Nodes	Cost
0	104	24874
1	222	21033
2	763	19967
3	1555	19587
4	2472	19505
done	5000	19425

prune508.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
20×	`times-frac`
19×	`add-exp-log`
17×	`associate-r`
13×	`add-cbrt-cube`
10×	`pow1`
6×	`log-prod` `associate-l`
5×	`prod-exp`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `cbrt-unprod` `associate-/l`
2×	`frac-times` `cbrt-undiv` `rec-exp` `flip3--` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `flip--`
1×	`clear-num` `frac-2neg` `associate-*r/` `log-pow` `un-div-inv` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 112

Calls

4 calls:

4.0ms	(/ 1 (fma (log base) (log base) (* 0.0 0.0)))
41.0ms	(* (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (/ 1 (fma (log base) (log base) (* 0.0 0.0))))
7.0ms	(* (atan2 im re) (log base))
0.0ms	(fma (log base) (log base) (* 0.0 0.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

500.0ms	(/ 1 (fma (log base) (log base) (* 0.0 0.0)))
115.0ms	(* (- (* (atan2 im re) (log base)) (* (log (hypot re im)) 0.0)) (/ 1 (fma (log base) (log base) (* 0.0 0.0))))
49.0ms	(* (atan2 im re) (log base))
451.0ms	(fma (log base) (log base) (* 0.0 0.0))

simplify4.8s

Counts

124 → 124

Iterations

Useful iterations: 3 (2.5s)

Iter	Nodes	Cost
0	187	60261
1	417	54132
2	1235	51699
3	4239	51369
done	5000	51369

prune851.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes478.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	253
done	6	253

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.5s	8000×	body	80	valid
1.3s	7971×	body	80	nan