Details

sample22.0ms

Algorithm

intervals

Results

11.0ms

272×

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
28.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

2.0ms	(+ (* 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)))

series113.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* x.re y.re) (* x.im y.im))
83.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify83.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2851	412
3	5003	412

prune146.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 28.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
18.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

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:

2.0ms	(+ (* x.re y.re) (* x.im y.im))
12.0ms	(/ (+ (* 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)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* x.re y.re) (* x.im y.im))
107.0ms	(/ (+ (* 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)))

simplify84.0ms

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

prune287.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 25.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
18.7b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
31.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.4b	(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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
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:

2.0ms	(+ (* x.re y.re) (* x.im y.im))
10.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* x.re y.re) (* x.im y.im))
86.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
38.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	263	883
1	831	838
2	2301	838
3	5001	838

prune326.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ (* x.re y.re) (* x.im y.im))
0.8b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
28.0b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
55×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`flip3-+` `flip-+`
6×	`div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

3 → 126

Calls

3 calls:

2.0ms	(+ (* x.re y.re) (* x.im y.im))
12.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
11.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* x.re y.re) (* x.im y.im))
145.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
53.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	480	1744
1	2237	1592
2	5003	1505

prune262.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.6b

regimes211.0ms

Accuracy

29.2% (2.2b remaining)

Error of 25.6b against oracle of 23.5b and baseline of 26.5b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	19
1	20	19

end0.0ms

sample511.0ms

Algorithm

intervals

Results

292.0ms

8457×

body

valid