Details

sample37.0ms

Algorithm

intervals

Results

18.0ms

270×

body

valid

simplify74.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	19	15
2	36	15
3	48	15
4	66	15
5	70	15
done	70	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
25.4b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite78.0ms

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`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

24.0ms	(+ (* y.re y.re) (* y.im y.im))
16.0ms	(- (* x.im y.re) (* x.re y.im))
35.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series251.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* y.re y.re) (* y.im y.im))
53.0ms	(- (* x.im y.re) (* x.re y.im))
158.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify3.4s

Counts

64 → 64

Iterations

Useful iterations: 2 (228.0ms)

Iter	Nodes	Cost
0	102	1120
1	290	1097
2	959	981
3	3121	981
done	5001	981

prune268.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
13.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite96.0ms

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`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

16.0ms	(- (* x.im y.re) (* x.re y.im))
52.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* x.im y.re) (* x.re y.im))
196.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
72.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.1s

Counts

98 → 98

Iterations

Useful iterations: 3 (691.0ms)

Iter	Nodes	Cost
0	121	1814
1	306	1682
2	888	1574
3	2539	1558
done	5001	1558

prune420.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 23.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
13.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite108.0ms

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`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

17.0ms	(- (* x.im y.re) (* x.re y.im))
55.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* x.im y.re) (* x.re y.im))
197.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
61.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
73.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.2s

Counts

98 → 98

Iterations

Useful iterations: 3 (628.0ms)

Iter	Nodes	Cost
0	121	1814
1	306	1682
2	888	1574
3	2539	1558
done	5001	1558

prune477.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 23.5b

localize32.0ms

Local error

Found 4 expressions with local error:

13.8b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`sqrt-prod`
18×	`times-frac`
8×	`sqrt-div`
7×	`pow1`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 89

Calls

4 calls:

55.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

101 → 101

Iterations

Useful iterations: 3 (516.0ms)

Iter	Nodes	Cost
0	108	1859
1	271	1705
2	749	1595
3	2007	1573
done	5000	1573

prune352.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 23.5b

regimes187.0ms

Accuracy

0% (2.8b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	16	25
done	16	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

750.0ms

8479×

body

valid