Details

sample35.0ms

Algorithm

intervals

Results

15.0ms

276×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
1	15
0	11

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize22.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
27.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
45.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series153.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(+ (* x.re y.re) (* x.im y.im))
103.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
3	4323
2	906
1	237
0	86

prune263.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
15.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

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:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
29.0ms	(/ (+ (* 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)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* x.re y.re) (* x.im y.im))
182.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.2s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1173
1	280
0	117

prune726.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* y.im x.im) (* y.re x.re))
15.3b	(/ (+ (* y.im x.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite95.0ms

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	(+ (* y.im x.im) (* y.re x.re))
57.0ms	(/ (+ (* y.im x.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* y.im x.im) (* y.re x.re))
152.0ms	(/ (+ (* y.im x.im) (* y.re x.re)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	4746
2	1003
1	278
0	114

prune833.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.6b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* y.im x.im) (* y.re x.re))
15.4b	(* (+ (* y.im x.im) (* y.re x.re)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

6.0ms	(+ (* y.im x.im) (* y.re x.re))
69.0ms	(* (+ (* y.im x.im) (* y.re x.re)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (* y.im x.im) (* y.re x.re))
154.0ms	(* (+ (* y.im x.im) (* y.re x.re)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
70.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify3.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	2281
1	406
0	143

prune609.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.6b

regimes649.0ms

Accuracy

21.4% (2.9b remaining)

Error of 25.0b against oracle of 22.1b and baseline of 25.8b

bsearch3.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8473×

body

valid