Details

sample38.0ms

Algorithm

intervals

Results

17.0ms

270×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
24.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite65.0ms

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` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 53

Calls

3 calls:

10.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(+ (* x.re y.re) (* x.im y.im))
42.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ (* y.re y.re) (* y.im y.im))
53.0ms	(+ (* 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)))

simplify756.0ms

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
2	1625
1	296
0	98

prune515.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.im y.im) (* y.re x.re))
16.4b	(/ (+ (* x.im y.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (pow y.im 2))))
28.9b	(sqrt (+ (* y.re y.re) (pow y.im 2)))
28.9b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `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` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

11.0ms	(+ (* x.im y.im) (* y.re x.re))
56.0ms	(/ (+ (* x.im y.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (pow y.im 2))))
17.0ms	(sqrt (+ (* y.re y.re) (pow y.im 2)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (* x.im y.im) (* y.re x.re))
181.0ms	(/ (+ (* x.im y.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (pow y.im 2))))
54.0ms	(sqrt (+ (* y.re y.re) (pow y.im 2)))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify597.0ms

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1239
1	334
0	142

prune714.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (pow y.im 2))
0.3b	(/ 1 (+ (* y.re y.re) (pow y.im 2)))
0.5b	(+ (* x.re y.re) (* x.im y.im))
24.7b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (pow y.im 2))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

8.0ms	(+ (* y.re y.re) (pow y.im 2))
16.0ms	(/ 1 (+ (* y.re y.re) (pow y.im 2)))
6.0ms	(+ (* x.re y.re) (* x.im y.im))
69.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (pow y.im 2))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* y.re y.re) (pow y.im 2))
51.0ms	(/ 1 (+ (* y.re y.re) (pow y.im 2)))
37.0ms	(+ (* x.re y.re) (* x.im y.im))
91.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (pow y.im 2))))

simplify3.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	3551
1	413
0	138

prune595.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 22.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (pow y.im 2))
0.5b	(+ (* x.im y.im) (* y.re x.re))
0.9b	(/ 1 (/ (+ (* y.re y.re) (pow y.im 2)) (+ (* x.im y.im) (* y.re x.re))))
24.3b	(/ (+ (* y.re y.re) (pow y.im 2)) (+ (* x.im y.im) (* y.re x.re)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

10.0ms	(+ (* y.re y.re) (pow y.im 2))
6.0ms	(+ (* x.im y.im) (* y.re x.re))
42.0ms	(/ 1 (/ (+ (* y.re y.re) (pow y.im 2)) (+ (* x.im y.im) (* y.re x.re))))
40.0ms	(/ (+ (* y.re y.re) (pow y.im 2)) (+ (* x.im y.im) (* y.re x.re)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* y.re y.re) (pow y.im 2))
51.0ms	(+ (* x.im y.im) (* y.re x.re))
174.0ms	(/ 1 (/ (+ (* y.re y.re) (pow y.im 2)) (+ (* x.im y.im) (* y.re x.re))))
82.0ms	(/ (+ (* y.re y.re) (pow y.im 2)) (+ (* x.im y.im) (* y.re x.re)))

simplify1.1s

Counts

149 → 149

Iterations

Iter	Nodes
done	5001
2	3575
1	573
0	204

prune542.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 22.6b

regimes406.0ms

Accuracy

0% (3.0b remaining)

Error of 26.0b against oracle of 23.0b and baseline of 26.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

686.0ms

8493×

body

valid