Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

272×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	7

prune3.0ms

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: 26.0b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
25.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 12

Calls

2 calls:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series118.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(+ (* x.re y.re) (* x.im y.im))
84.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify148.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	122	84
1	404	80
2	1407	79
3	4726	79
4	5001	79

prune59.0ms

Filtered

18 candidates to 15 candidates (83.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	12	6	18
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	7	19

Merged error: 25.4b

Counts

19 → 7

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
0.3b	(+ (* x.re y.re) (* x.im y.im))
25.5b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 25

Calls

3 calls:

8.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
4.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series221.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
30.0ms	(+ (* x.re y.re) (* x.im y.im))
54.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify65.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	164	153
1	598	142
2	2483	133
3	5001	132

prune96.0ms

Filtered

34 candidates to 27 candidates (79.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	33	8	41

Merged error: 25.3b

Counts

41 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
0.3b	(/ 1 (fma y.re y.re (* y.im y.im)))
0.6b	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
25.5b	(/ (/ 1 (fma y.re y.re (* y.im y.im))) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-/r/` `div-inv`
5×	`frac-2neg` `clear-num`
4×	`flip3-+` `flip-+`
3×	`times-frac` `associate-/r*` `associate-/l/`
2×	`fma-def` `inv-pow`
1×	`+-commutative` `-commutative` `associate-/l`

Counts

4 → 31

Calls

4 calls:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
2.0ms	(/ 1 (fma y.re y.re (* y.im y.im)))
4.0ms	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
7.0ms	(/ (/ 1 (fma y.re y.re (* y.im y.im))) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* x.re y.re) (* x.im y.im))
41.0ms	(/ 1 (fma y.re y.re (* y.im y.im)))
26.0ms	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
144.0ms	(/ (/ 1 (fma y.re y.re (* y.im y.im))) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

simplify63.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	137	175
1	557	161
2	2162	160
3	5001	160

prune102.0ms

Filtered

43 candidates to 27 candidates (62.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	43	8	51

Merged error: 25.3b

Counts

51 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.re y.re) (* x.im y.im))
0.2b	(- (* x.re y.re) (* x.im y.im))
25.7b	(/ (/ (* (fma x.re y.re (* x.im y.im)) (- (* x.re y.re) (* x.im y.im))) (fma y.re y.re (* y.im y.im))) (- (* x.re y.re) (* x.im y.im)))
30.6b	(/ (* (fma x.re y.re (* x.im y.im)) (- (* x.re y.re) (* x.im y.im))) (fma y.re y.re (* y.im y.im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-commutative`
11×	`associate-/l/`
8×	`prod-diff`
5×	`flip3--` `flip--` `associate-/l*`
4×	`fma-neg` `associate-*r/`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`sub-neg` `associate-/r/`

Counts

4 → 40

Calls

4 calls:

5.0ms	(- (* x.re y.re) (* x.im y.im))
4.0ms	(- (* x.re y.re) (* x.im y.im))
10.0ms	(/ (/ (* (fma x.re y.re (* x.im y.im)) (- (* x.re y.re) (* x.im y.im))) (fma y.re y.re (* y.im y.im))) (- (* x.re y.re) (* x.im y.im)))
8.0ms	(/ (* (fma x.re y.re (* x.im y.im)) (- (* x.re y.re) (* x.im y.im))) (fma y.re y.re (* y.im y.im)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* x.re y.re) (* x.im y.im))
36.0ms	(- (* x.re y.re) (* x.im y.im))
89.0ms	(/ (/ (* (fma x.re y.re (* x.im y.im)) (- (* x.re y.re) (* x.im y.im))) (fma y.re y.re (* y.im y.im))) (- (* x.re y.re) (* x.im y.im)))
150.0ms	(/ (* (fma x.re y.re (* x.im y.im)) (- (* x.re y.re) (* x.im y.im))) (fma y.re y.re (* y.im y.im)))

simplify121.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	171	313
1	720	306
2	4578	272
3	5001	271

prune117.0ms

Filtered

52 candidates to 34 candidates (65.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	50	10	60

Merged error: 18.2b

Counts

60 → 10

regimes225.0ms

Accuracy

31.5% (4.8b remaining)

Error of 23.9b against oracle of 19.1b and baseline of 26.1b

bsearch85.0ms

Steps

Iters	Range		Point
9	9.768553005369636e+133	6.764184952264426e+138	6.670795820110577e+138
9	-1.9658258378654302e+115	-1.957298096855346e+110	-1.9497673481821607e+115

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	13
1	34	13
2	34	13

end0.0ms

sample519.0ms

Algorithm

intervals

Results

308.0ms

8441×

body

valid