Details

sample33.0ms

Algorithm

intervals

Results

21.0ms

268×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	15
1	15
0	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.0b	(+ (* x.re y.re) (* x.im y.im))
27.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 56

Calls

3 calls:

13.0ms	(+ (* y.re y.re) (* y.im y.im))
7.0ms	(+ (* x.re y.re) (* x.im y.im))
38.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* y.re y.re) (* y.im y.im))
45.0ms	(+ (* x.re y.re) (* x.im y.im))
123.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts

65 → 65

Iterations

Iter	Nodes
3	4222
2	1140
1	284
0	101

prune433.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
18.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*` `flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 268

Calls

4 calls:

47.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
49.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
174.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.5s

Counts

280 → 280

Iterations

Iter	Nodes
3	6045
2	1718
1	721
0	305

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 25.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (* 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))))
18.7b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
28×	`times-frac` `add-exp-log`
26×	`*-un-lft-identity`
24×	`associate-r` `add-cube-cbrt`
23×	`sqrt-prod`
18×	`add-cbrt-cube`
9×	`div-exp`
8×	`pow1` `flip3-+` `sqrt-div` `prod-exp` `flip-+`
6×	`associate-/r*` `associate-/l/`
5×	`cbrt-undiv` `unswap-sqr`
4×	`frac-times` `associate-*l/` `associate-/r/` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-l`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-*r/` `un-div-inv` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l`

Counts

4 → 126

Calls

4 calls:

35.0ms	(/ (* (+ (* 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))))
61.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
21.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (* (+ (* 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))))
137.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify6.2s

Counts

138 → 138

Iterations

Iter	Nodes
3	5836
2	1663
1	510
0	181

prune653.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
18.6b	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*` `flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 268

Calls

4 calls:

40.0ms	(/ (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
50.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
144.0ms	(/ (+ (* x.im y.im) (* x.re y.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.7s

Counts

280 → 280

Iterations

Iter	Nodes
3	6040
2	1718
1	721
0	305

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.5b

regimes426.0ms

Accuracy

0% (3.1b remaining)

Error of 25.7b against oracle of 22.5b and baseline of 25.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	17
1	17
0	13

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8453×

body

valid