Details

sample19.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
1	7
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
30.3b	(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

13.0ms	(+ (* re re) (* im im))
12.0ms	(sqrt (+ (* re re) (* im im)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(+ (* re re) (* im im))
65.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.7s

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
3	1599
2	373
1	129
0	50

prune162.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 7.8b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.6b	(exp (log (sqrt (+ (* re re) (* im im)))))
30.3b	(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `log-prod` `exp-prod` `exp-sum` `sqrt-prod`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`flip3-+` `add-cbrt-cube` `add-exp-log` `log-pow` `flip-+` `insert-posit16`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `rem-exp-log`

Counts

3 → 51

Calls

3 calls:

8.0ms	(+ (* re re) (* im im))
11.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
8.0ms	(sqrt (+ (* re re) (* im im)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (* re re) (* im im))
60.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
51.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.2s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
3	1435
2	428
1	180
0	90

prune226.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize32.0ms

Local error

Found 4 expressions with local error:

5.9b	(pow (exp (* (cbrt (log (sqrt (+ (* re re) (* im im))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))
30.3b	(sqrt (+ (* re re) (* im im)))
30.3b	(sqrt (+ (* re re) (* im im)))
30.3b	(sqrt (+ (* re re) (* im im)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow-unpow` `sqrt-prod`
6×	`cbrt-prod` `sqrt-div`
5×	`add-log-exp`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16`
3×	`rem-sqrt-square` `unpow-prod-down` `pow-pow` `flip3-+` `log-pow` `flip-+`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

10.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* re re) (* im im))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))
20.0ms	(sqrt (+ (* re re) (* im im)))
15.0ms	(sqrt (+ (* re re) (* im im)))
15.0ms	(sqrt (+ (* re re) (* im im)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(pow (exp (* (cbrt (log (sqrt (+ (* re re) (* im im))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))) (cbrt (log (sqrt (+ (* re re) (* im im))))))
57.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))
52.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.5s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
3	1554
2	540
1	230
0	92

prune464.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize60.0ms

Local error

Found 4 expressions with local error:

30.3b	(sqrt (+ (* re re) (* im im)))
30.3b	(sqrt (+ (* re re) (* im im)))
30.3b	(sqrt (+ (* re re) (* im im)))
30.3b	(sqrt (+ (* re re) (* im im)))

rewrite47.0ms

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:

8.0ms	(sqrt (+ (* re re) (* im im)))
14.0ms	(sqrt (+ (* re re) (* im im)))
15.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ (* re re) (* im im)))
40.0ms	(sqrt (+ (* re re) (* im im)))
55.0ms	(sqrt (+ (* re re) (* im im)))
41.0ms	(sqrt (+ (* re re) (* im im)))

simplify2.7s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
5	3254
4	995
3	435
2	196
1	92
0	39

prune637.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.8b

regimes602.0ms

Accuracy

58.7% (9.1b remaining)

Error of 16.5b against oracle of 7.5b and baseline of 29.4b

bsearch43.0ms

Steps

Iters	Range		Point
6	7.119865998070051e+107	7.387240647586424e+108	7.263939058947569e+108
4	-8.257930834154903e+96	-5.807654414909257e+96	-8.181359696053478e+96

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	13

end0.0ms

sample620.0ms

Algorithm

intervals

Results

466.0ms

8000×

body

valid