Details

analyze441.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

sample39.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
3.0ms	32×	body	80	nan

simplify167.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (165.0ms)

Iter	Nodes	Cost
0	4829	28
1	4829	28

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.4b

Counts

2 → 1

localize22.0ms

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)))
0.4b	(* (atan2 im re) (log base))
0.6b	(* (log base) (log base))
29.1b	(sqrt (+ (* re re) (* im im)))

rewrite25.0ms

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:

9.0ms	(/ (- (* (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))
5.0ms	(* (log base) (log base))
4.0ms	(sqrt (+ (* re re) (* im im)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (- (* (atan2 im re) (log base)) (* (log (sqrt (+ (* re re) (* im im)))) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
8.0ms	(* (atan2 im re) (log base))
15.0ms	(* (log base) (log base))
6.0ms	(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4942	1828
1	4942	1828

prune237.0ms

Filtered

80 candidates to 120 candidates (-50.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	12	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Merged error: 0.1b

Counts

121 → 12

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`associate-/r*` `log-pow`
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 → 31

Calls

1 calls:

3.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify59.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4938	330
1	4938	330

prune92.0ms

Filtered

22 candidates to 34 candidates (-54.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	27	7	34
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	31	15	46

Merged error: 0.0b

Counts

46 → 15

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)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`pow1` `associate-/r*`
16×	`log-pow`
15×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

2 → 119

Calls

2 calls:

4.0ms	(/ (log base) (atan2 im re))
7.0ms	(/ 1 (/ (log base) (atan2 im re)))

series24.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(/ (log base) (atan2 im re))
12.0ms	(/ 1 (/ (log base) (atan2 im re)))

simplify65.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5227	1473

prune124.0ms

Filtered

62 candidates to 125 candidates (-101.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	5	8	13
Picked	0	1	1
Done	0	1	1
Total	127	13	140

Merged error: 0.0b

Counts

140 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ (atan2 im re) (log base))) (cbrt (/ (atan2 im re) (log base))))
5.1b	(cbrt (/ (atan2 im re) (log base)))
5.1b	(cbrt (/ (atan2 im re) (log base)))
5.1b	(cbrt (/ (atan2 im re) (log base)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

136×	`cbrt-prod`
102×	`times-frac`
92×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
68×	`add-cube-cbrt`
38×	`pow1`
27×	`log-pow`
25×	`swap-sqr`
19×	`associate-r` `associate-l`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 168

Calls

4 calls:

17.0ms	(* (cbrt (/ (atan2 im re) (log base))) (cbrt (/ (atan2 im re) (log base))))
2.0ms	(cbrt (/ (atan2 im re) (log base)))
2.0ms	(cbrt (/ (atan2 im re) (log base)))
3.0ms	(cbrt (/ (atan2 im re) (log base)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cbrt (/ (atan2 im re) (log base))) (cbrt (/ (atan2 im re) (log base))))
22.0ms	(cbrt (/ (atan2 im re) (log base)))
22.0ms	(cbrt (/ (atan2 im re) (log base)))
22.0ms	(cbrt (/ (atan2 im re) (log base)))

simplify68.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5080	2732

prune140.0ms

Filtered

119 candidates to 180 candidates (-51.3%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	180	13	193

Merged error: 0.0b

Counts

193 → 13

regimes366.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	6	6

end0.0ms

sample1.1s

Algorithm

intervals

Results

779.0ms	8000×	body	80	valid
94.0ms	1036×	body	80	nan

Details

analyze441.0ms

sample39.0ms

simplify167.0ms

prune5.0ms

localize22.0ms

rewrite25.0ms

series40.0ms

simplify47.0ms

prune237.0ms

localize7.0ms

rewrite4.0ms

series10.0ms

simplify59.0ms

prune92.0ms

localize9.0ms

rewrite16.0ms

series24.0ms

simplify65.0ms

prune124.0ms

localize11.0ms

rewrite33.0ms

series106.0ms

simplify68.0ms

prune140.0ms

regimes366.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling