Details

sample55.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
17.0ms	266×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	16
1	23	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: 27.5b

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))
25.4b	(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 14

Calls

4 calls:

9.0ms	(/ (+ (* (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))
4.0ms	(sqrt (+ (* re re) (* im im)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
93.0ms	(* (log (sqrt (+ (* re re) (* im im)))) (log base))
149.0ms	(* (log base) (log base))
35.0ms	(sqrt (+ (* re re) (* im im)))

simplify69.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	217	206
1	641	202
2	2188	200
3	5002	192

prune123.0ms

Filtered

26 candidates to 21 candidates (80.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	16	10	26
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	17	10	27

Merged error: 7.3b

Counts

27 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.4b	(* (log (+ (* re re) (* im im))) (log base))
0.5b	(* (log base) (log base))
26.4b	(log (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
3.0ms	(* (log (+ (* re re) (* im im))) (log base))
3.0ms	(* (log base) (log base))
4.0ms	(log (+ (* re re) (* im im)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
77.0ms	(* (log (+ (* re re) (* im im))) (log base))
147.0ms	(* (log base) (log base))
46.0ms	(log (+ (* re re) (* im im)))

simplify94.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	237	211
1	732	205
2	3052	198
3	5001	194

prune111.0ms

Filtered

24 candidates to 15 candidates (62.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	17	7	24
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	23	11	34

Merged error: 7.3b

Counts

34 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)))
0.4b	(* (log (+ (* re re) (* im im))) (log base))
0.5b	(* (log base) (log base))
26.4b	(log (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)))
3.0ms	(* (log (+ (* re re) (* im im))) (log base))
3.0ms	(* (log base) (log base))
4.0ms	(log (+ (* re re) (* im im)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* (atan2 im re) 0.0)))
78.0ms	(* (log (+ (* re re) (* im im))) (log base))
153.0ms	(* (log base) (log base))
52.0ms	(log (+ (* re re) (* im im)))

simplify86.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	245	212
1	760	207
2	2998	201
3	5001	196

prune140.0ms

Filtered

24 candidates to 19 candidates (79.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	19	5	24
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	19	16	35

Merged error: 7.2b

Counts

35 → 16

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* 1/2 (* (log (+ (* re re) (* im im))) (log base))))
26.4b	(log (+ (* re re) (* im im)))
26.4b	(log (+ (* re re) (* im im)))
26.4b	(log (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-r`
9×	`*-commutative`
6×	`log-div`
4×	`swap-sqr` `associate-l`
3×	`flip3-+` `flip-+`
1×	`pow2`

Counts

4 → 20

Calls

4 calls:

9.0ms	(* (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* 1/2 (* (log (+ (* re re) (* im im))) (log base))))
4.0ms	(log (+ (* re re) (* im im)))
4.0ms	(log (+ (* re re) (* im im)))
4.0ms	(log (+ (* re re) (* im im)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (* 1/2 (* (log (+ (* re re) (* im im))) (log base))) (* 1/2 (* (log (+ (* re re) (* im im))) (log base))))
52.0ms	(log (+ (* re re) (* im im)))
53.0ms	(log (+ (* re re) (* im im)))
48.0ms	(log (+ (* re re) (* im im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	190	273
1	563	263
2	2053	262
3	5001	259

prune179.0ms

Filtered

32 candidates to 31 candidates (96.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	4	10	14
Picked	0	1	1
Done	1	0	1
Total	33	15	48

Merged error: 7.1b

Counts

48 → 15

regimes482.0ms

Accuracy

58.8% (9.8b remaining)

Error of 17.5b against oracle of 7.7b and baseline of 31.5b

bsearch178.0ms

Steps

Iters	Range		Point
9	1.05009971062057e+89	2.2266410785879893e+96	7.023692837103527e+90
9	-1.0758192247430045e+113	-7.81690939864499e+104	-3.4790806105029457e+108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	53
1	66	53
2	66	53

end0.0ms

sample1.4s

Algorithm

intervals

Results

553.0ms	8000×	body	80	valid
530.0ms	8159×	body	80	nan