Details

sample31.0ms

Algorithm

intervals

Results

13.0ms

269×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.3b

Counts

2 → 1

localize15.0ms

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

rewrite19.0ms

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

Counts

3 → 53

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series46.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* y.re y.re) (* y.im y.im))
11.0ms	(+ (* x.re y.re) (* x.im y.im))
29.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify840.0ms

Counts

62 → 62

Iterations

Useful iterations: 3 (310.0ms)

Iter	Nodes	Cost
0	99	1090
1	282	1068
2	1049	954
3	2963	951
done	5000	951

prune126.0ms

Filtered

49 candidates to 62 candidates (-26.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	52	10	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	10	63

Merged error: 27.5b

Counts

63 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* y.re x.re) (* x.im y.im))
17.9b	(/ (+ (* y.re x.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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:

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

series54.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* y.re x.re) (* x.im y.im))
31.0ms	(/ (+ (* y.re x.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)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify659.0ms

Counts

96 → 96

Iterations

Useful iterations: 3 (231.0ms)

Iter	Nodes	Cost
0	116	1780
1	281	1658
2	802	1544
3	2191	1525
done	5000	1525

prune139.0ms

Filtered

77 candidates to 96 candidates (-24.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	96	10	106

Merged error: 23.8b

Counts

106 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* y.re x.re) (* x.im y.im))
17.9b	(/ (+ (* y.re x.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms

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:

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

series52.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* y.re x.re) (* x.im y.im))
29.0ms	(/ (+ (* y.re x.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)))

simplify663.0ms

Counts

96 → 96

Iterations

Useful iterations: 3 (237.0ms)

Iter	Nodes	Cost
0	116	1780
1	281	1658
2	802	1544
3	2191	1525
done	5000	1525

prune139.0ms

Filtered

77 candidates to 96 candidates (-24.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	96	10	106

Merged error: 23.8b

Counts

106 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.im y.im) (* y.re y.re))
0.5b	(+ (* y.re x.re) (* x.im y.im))
1.0b	(/ 1 (/ (+ (* y.im y.im) (* y.re y.re)) (+ (* y.re x.re) (* x.im y.im))))
27.1b	(/ (+ (* y.im y.im) (* y.re y.re)) (+ (* y.re x.re) (* x.im y.im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

4.0ms	(+ (* y.im y.im) (* y.re y.re))
4.0ms	(+ (* y.re x.re) (* x.im y.im))
10.0ms	(/ 1 (/ (+ (* y.im y.im) (* y.re y.re)) (+ (* y.re x.re) (* x.im y.im))))
12.0ms	(/ (+ (* y.im y.im) (* y.re y.re)) (+ (* y.re x.re) (* x.im y.im)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* y.im y.im) (* y.re y.re))
11.0ms	(+ (* y.re x.re) (* x.im y.im))
29.0ms	(/ 1 (/ (+ (* y.im y.im) (* y.re y.re)) (+ (* y.re x.re) (* x.im y.im))))
20.0ms	(/ (+ (* y.im y.im) (* y.re y.re)) (+ (* y.re x.re) (* x.im y.im)))

simplify639.0ms

Counts

149 → 149

Iterations

Useful iterations: done (634.0ms)

Iter	Nodes	Cost
0	206	3676
1	530	3480
2	2076	3194
done	5000	3111

prune109.0ms

Filtered

88 candidates to 149 candidates (-69.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	149	10	159

Merged error: 23.8b

Counts

159 → 10

regimes489.0ms

Accuracy

40.8% (1.9b remaining)

Error of 25.6b against oracle of 23.7b and baseline of 27.0b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	83
1	32	83
done	32	83

end0.0ms

sample881.0ms

Algorithm

intervals

Results

433.0ms

8479×

body

valid

Details

sample31.0ms

simplify4.0ms

prune4.0ms

localize15.0ms

rewrite19.0ms

series46.0ms

simplify840.0ms

prune126.0ms

localize13.0ms

rewrite25.0ms

series54.0ms

simplify659.0ms

prune139.0ms

localize15.0ms

rewrite25.0ms

series52.0ms

simplify663.0ms

prune139.0ms

localize12.0ms

rewrite36.0ms

series66.0ms

simplify639.0ms

prune109.0ms

regimes489.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample881.0ms

Profiling