Details

sample50.0ms

Algorithm

intervals

Results

16.0ms

273×

body

valid

simplify233.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize33.0ms

Local error

Found 2 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
24.9b	(/ (- (* x.im y.re) (* x.re 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` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

2 → 46

Calls

2 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
39.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series272.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (* x.im y.re) (* x.re y.im))
208.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify5.7s

Counts

52 → 52

Iterations

Iter	Nodes
done	5002
3	3063
2	901
1	259
0	91

prune796.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* x.im y.re) (* x.re y.im))
15.0b	(/ (- (* x.im y.re) (* x.re 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)))

rewrite110.0ms

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`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

20.0ms	(- (* x.im y.re) (* x.re y.im))
39.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* x.im y.re) (* x.re y.im))
288.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
65.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
67.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify4.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5004
3	2697
2	922
1	315
0	124

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.7b

localize150.0ms

Local error

Found 4 expressions with local error:

29.3b	(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)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

21.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
22.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
21.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
18.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
63.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
81.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify6.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
5	3240
4	991
3	433
2	196
1	92
0	39

prune1.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 21.7b

localize77.0ms

Local error

Found 4 expressions with local error:

10.3b	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
10.3b	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
24.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
24.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
30×	`sqrt-prod`
8×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
6×	`pow1` `associate-/r` `associate-/l`
4×	`rem-sqrt-square` `flip3-+` `flip-+` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `div-exp` `flip--`

Counts

4 → 122

Calls

4 calls:

46.0ms	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
45.0ms	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
63.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
70.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series1.0s

Counts

4 → 12

Calls

4 calls:

332.0ms	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
274.0ms	(sqrt (/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im))))
243.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
197.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify5.1s

Counts

134 → 134

Iterations

Iter	Nodes
done	5003
3	2694
2	822
1	284
0	118

prune2.0s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 21.7b

regimes1.7s

Accuracy

3.5% (2.8b remaining)

Error of 26.0b against oracle of 23.1b and baseline of 26.1b

bsearch89.0ms

Steps

Iters	Range		Point
9	1.36934023547096e+82	3.0707098332476226e+88	7.672387965946081e+87

simplify14.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample1.2s

Algorithm

intervals

Results

758.0ms

8506×

body

valid