Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

275×

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: 26.9b

Counts

2 → 1

localize10.0ms

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))
26.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite19.0ms

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

series137.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
79.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify126.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (27.0ms)

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: 26.1b

Counts

63 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
17.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite21.0ms

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:

3.0ms	(+ (* 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)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x.re y.re) (* x.im y.im))
102.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

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

prune231.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	93	11	104

Merged error: 23.8b

Counts

104 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.2b	(+ (* x.re y.re) (* x.im y.im))
0.7b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
26.0b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `1-exp` `associate-*l/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 97

Calls

4 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series175.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
30.0ms	(+ (* x.re y.re) (* x.im y.im))
36.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
78.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify57.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	393	853
1	2037	749
2	5003	720

prune213.0ms

Filtered

109 candidates to 69 candidates (63.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	109	11	120

Merged error: 23.8b

Counts

120 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
26.0b	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
173×	`add-sqr-sqrt`
150×	`associate-r`
141×	`sqrt-prod`
138×	`*-un-lft-identity`
134×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`sqrt-div`
14×	`associate-/r/`
13×	`add-cbrt-cube`
12×	`flip3-+` `flip-+` `unswap-sqr`
8×	`pow1` `div-inv`
6×	`div-exp` `add-log-exp`
5×	`prod-exp`
3×	`cbrt-undiv` `associate-l` `cbrt-unprod`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`+-commutative` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `-commutative`

Counts

4 → 228

Calls

4 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
45.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.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)))

series183.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* x.re y.re) (* x.im y.im))
78.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	975	3429
1	5001	2870

prune429.0ms

Filtered

240 candidates to 128 candidates (53.3%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	240	11	251

Merged error: 23.8b

Counts

251 → 11

regimes217.0ms

Accuracy

33.3% (2.0b remaining)

Error of 25.0b against oracle of 23.1b and baseline of 26.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	26
1	28	26
2	28	26

end0.0ms

sample504.0ms

Algorithm

intervals

Results

293.0ms

8450×

body

valid