Details

sample49.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
15.0ms	220×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	33	16
2	33	16

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 30.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b	(* (log base) (log base))
28.0b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-commutative`
5×	`hypot-def`
3×	`flip3-+` `flip-+`
2×	`pow1/2` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`+-commutative` `pow2` `frac-2neg` `associate-l` `clear-num` `log-pow` `div-inv`

Counts

4 → 19

Calls

4 calls:

13.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
3.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
2.0ms	(* (log base) (log base))
5.0ms	(sqrt (+ (* re re) (* im im)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
92.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
151.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify70.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	229	206
1	701	198
2	2482	194
3	5002	186

prune134.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	21	10	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	10	32

Merged error: 0.2b

Counts

32 → 10

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/`
1×	`pow2` `frac-2neg` `clear-num` `div-inv`

Counts

3 → 10

Calls

3 calls:

11.0ms	(/ (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
2.0ms	(* (log (hypot im re)) (log base))
3.0ms	(* (log base) (log base))

series355.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(/ (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
99.0ms	(* (log (hypot im re)) (log base))
151.0ms	(* (log base) (log base))

simplify58.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	162	145
1	518	138
2	2015	136
3	5001	128

prune87.0ms

Filtered

19 candidates to 15 candidates (78.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	10	9	19
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	19	10	29

Merged error: 0.1b

Counts

29 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0))))
0.3b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)))
0.4b	(* (log (hypot im re)) (log base))
0.5b	(* (log base) (log base))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-/r/`
4×	`flip3-+` `clear-num` `flip-+` `associate-/l/`
3×	`frac-2neg` `associate-/r*` `div-inv`
2×	`*-commutative`
1×	`pow2` `remove-double-div` `inv-pow`

Counts

4 → 23

Calls

4 calls:

8.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0))))
8.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)))
2.0ms	(* (log (hypot im re)) (log base))
3.0ms	(* (log base) (log base))

series520.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ 1 (/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0))))
140.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)))
98.0ms	(* (log (hypot im re)) (log base))
150.0ms	(* (log base) (log base))

simplify99.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	210	275
1	747	261
2	3580	237
3	5001	230

prune159.0ms

Filtered

35 candidates to 28 candidates (80.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	27	8	35
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	34	11	45

Merged error: 0.0b

Counts

45 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
8×	`prod-diff`
6×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `associate-*r/`
1×	`pow-to-exp` `flip3--` `flip--` `unpow2` `sqr-pow`

Counts

4 → 20

Calls

4 calls:

3.0ms	(* (log (hypot im re)) (log base))
2.0ms	(* (log (hypot im re)) (log base))
1.0ms	(pow (log base) 2)
6.0ms	(* (fma (log (hypot im re)) (log base) (* (atan2 im re) 0.0)) (- (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (log (hypot im re)) (log base))
97.0ms	(* (log (hypot im re)) (log base))
145.0ms	(pow (log base) 2)
176.0ms	(* (fma (log (hypot im re)) (log base) (* (atan2 im re) 0.0)) (- (* (log (hypot im re)) (log base)) (* (atan2 im re) 0.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	170	397
1	570	396
2	2562	383
3	5001	371

prune94.0ms

Filtered

32 candidates to 18 candidates (56.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	32	11	43

Merged error: 0.0b

Counts

43 → 11

regimes399.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	26
1	21	26

end0.0ms

sample1.6s

Algorithm

intervals

Results

613.0ms	8000×	body	80	valid
573.0ms	8005×	body	80	nan