Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

264×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

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: 24.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(+ (* x.re y.re) (* x.im y.im))
23.6b	(/ (+ (* x.re y.re) (* x.im 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`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* 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)))

series132.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (* y.re y.re) (* y.im y.im))
31.0ms	(+ (* x.re y.re) (* x.im y.im))
76.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify128.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4451	477
3	5003	477

prune154.0ms

Filtered

62 candidates to 49 candidates (79.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	55	7	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	8	63

Merged error: 23.3b

Counts

63 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
16.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series207.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* x.re y.re) (* x.im y.im))
104.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify87.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2693	828
3	5001	828

prune246.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	92	12	104

Merged error: 21.2b

Counts

104 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
16.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 160

Calls

4 calls:

25.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
106.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	567	2505
1	3282	2242
2	5001	2117

prune367.0ms

Filtered

172 candidates to 110 candidates (64.0%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	171	13	184

Merged error: 21.2b

Counts

184 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

16.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
29.9b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
6×	`add-exp-log` `cbrt-prod` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+`
4×	`cbrt-div` `sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

10.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
95.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
94.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify131.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	294	963
1	1015	902
2	4043	887
3	5002	885

prune305.0ms

Filtered

96 candidates to 76 candidates (79.2%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	1	8	9
Picked	0	1	1
Done	0	3	3
Total	95	14	109

Merged error: 21.2b

Counts

109 → 14

regimes269.0ms

Accuracy

27.5% (2.2b remaining)

Error of 24.7b against oracle of 22.5b and baseline of 25.5b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	27
1	35	27
2	38	27
3	40	27
4	40	27

end0.0ms

sample509.0ms

Algorithm

intervals

Results

297.0ms

8497×

body

valid