Details

analyze506.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample24.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
1.0ms	15×	body	80	invalid

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4752	15
1	4752	15

prune4.0ms

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: 24.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
24.1b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 54

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series44.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(- (* x.im y.re) (* x.re y.im))
29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	6330	976

prune119.0ms

Filtered

49 candidates to 63 candidates (-28.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	54	9	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	9	64

Merged error: 18.9b

Counts

64 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

2.3b	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
2.9b	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
17.0b	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
17.1b	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
6×	`associate-l` `associate-/r` `associate-/l`
4×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 126

Calls

4 calls:

9.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
11.0ms	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
14.0ms	(* x.im (/ y.re (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(/ y.re (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5022	1682

prune202.0ms

Filtered

108 candidates to 138 candidates (-27.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	132	6	138
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	135	12	147

Merged error: 18.9b

Counts

147 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

2.3b	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
2.9b	(* x.im (/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) y.re)))
16.9b	(/ (+ (* y.re y.re) (* y.im y.im)) y.re)
17.1b	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

100×	`times-frac`
83×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
64×	`add-cube-cbrt`
59×	`associate-r`
32×	`add-exp-log`
22×	`add-cbrt-cube`
10×	`div-exp`
9×	`prod-exp`
8×	`pow1`
7×	`div-inv` `unswap-sqr`
6×	`cbrt-undiv` `associate-l` `associate-/r` `associate-/l`
5×	`associate-/r/` `cbrt-unprod`
4×	`add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l/`
1×	`un-div-inv`

Counts

4 → 165

Calls

4 calls:

9.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
15.0ms	(* x.im (/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) y.re)))
6.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) y.re)
7.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
13.0ms	(* x.im (/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) y.re)))
8.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) y.re)
7.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

simplify47.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5233	2285

prune248.0ms

Filtered

134 candidates to 177 candidates (-32.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	177	12	189

Merged error: 11.3b

Counts

189 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ y.re (* y.im (/ y.im y.re))))
2.3b	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
2.9b	(* x.im (/ 1 (+ y.re (* y.im (/ y.im y.re)))))
17.1b	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
39×	`times-frac`
37×	`*-un-lft-identity`
36×	`add-cube-cbrt`
30×	`associate-r`
24×	`add-exp-log`
18×	`add-cbrt-cube`
9×	`pow1`
8×	`associate-/r/`
6×	`div-exp` `associate-l` `prod-exp` `associate-/r` `associate-/l`
5×	`unswap-sqr`
4×	`cbrt-undiv` `flip3-+` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `clear-num` `-commutative`
1×	`pow-flip` `un-div-inv` `inv-pow`

Counts

4 → 134

Calls

4 calls:

6.0ms	(/ 1 (+ y.re (* y.im (/ y.im y.re))))
9.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(* x.im (/ 1 (+ y.re (* y.im (/ y.im y.re)))))
5.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1 (+ y.re (* y.im (/ y.im y.re))))
14.0ms	(* x.re (/ y.im (+ (* y.re y.re) (* y.im y.im))))
11.0ms	(* x.im (/ 1 (+ y.re (* y.im (/ y.im y.re)))))
7.0ms	(/ y.im (+ (* y.re y.re) (* y.im y.im)))

simplify54.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4964	1692
1	4964	1692

prune147.0ms

Filtered

102 candidates to 146 candidates (-43.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	143	15	158

Merged error: 10.0b

Counts

158 → 15

regimes412.0ms

Accuracy

0% (2.3b remaining)

Error of 14.2b against oracle of 11.9b and baseline of 14.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	98	21
1	98	21

end0.0ms

sample618.0ms

Algorithm

intervals

Results

374.0ms	8000×	body	80	valid
22.0ms	495×	body	80	invalid

Details

analyze506.0ms

sample24.0ms

simplify116.0ms

prune4.0ms

localize9.0ms

rewrite16.0ms

series44.0ms

simplify55.0ms

prune119.0ms

localize11.0ms

rewrite34.0ms

series42.0ms

simplify61.0ms

prune202.0ms

localize12.0ms

rewrite43.0ms

series46.0ms

simplify47.0ms

prune248.0ms

localize14.0ms

rewrite32.0ms

series38.0ms

simplify54.0ms

prune147.0ms

regimes412.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample618.0ms

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