Details

sample19.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify5.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize21.0ms

Local error

Found 1 expressions with local error:

28.1b

(sqrt (+ (* re re) (* im im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 16

Calls

1 calls:

Slowest

13.0ms

(sqrt (+ (* re re) (* im im)))

series87.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

87.0ms

(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts: 19 → 19

prune211.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize37.0ms

Local error

Found 4 expressions with local error:

29.1b	(cbrt (+ (* re re) (* im im)))
29.1b	(cbrt (+ (* re re) (* im im)))
0.3b	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
0.1b	(sqrt (cbrt (+ (* re re) (* im im))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`cbrt-prod` `sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r`
8×	`cbrt-div`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
4×	`flip3-+` `sqrt-div` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow1/3` `associate-l` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/`
1×	`pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 78

Calls

4 calls:

Slowest

38.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
14.0ms	(cbrt (+ (* re re) (* im im)))
8.0ms	(cbrt (+ (* re re) (* im im)))
7.0ms	(sqrt (cbrt (+ (* re re) (* im im))))

series512.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
134.0ms	(cbrt (+ (* re re) (* im im)))
125.0ms	(cbrt (+ (* re re) (* im im)))
116.0ms	(sqrt (cbrt (+ (* re re) (* im im))))

simplify961.0ms

Counts: 90 → 90

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize21.0ms

Local error

Found 4 expressions with local error:

28.1b	(sqrt (+ (* re re) (* im im)))
28.1b	(sqrt (+ (* re re) (* im im)))
28.1b	(sqrt (+ (* re re) (* im im)))
0.5b	(cbrt (sqrt (+ (* re re) (* im im))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

Slowest

13.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
4.0ms	(cbrt (sqrt (+ (* re re) (* im im))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
61.0ms	(sqrt (+ (* re re) (* im im)))
54.0ms	(sqrt (+ (* re re) (* im im)))
52.0ms	(sqrt (+ (* re re) (* im im)))

simplify992.0ms

Counts: 77 → 77

prune787.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize55.0ms

Local error

Found 4 expressions with local error:

28.1b	(sqrt (+ (* re re) (* im im)))
28.1b	(sqrt (+ (* re re) (* im im)))
28.1b	(sqrt (+ (* re re) (* im im)))
28.1b	(sqrt (+ (* re re) (* im im)))

rewrite35.0ms

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:

Slowest

11.0ms	(sqrt (+ (* re re) (* im im)))
10.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

68.0ms	(sqrt (+ (* re re) (* im im)))
61.0ms	(sqrt (+ (* re re) (* im im)))
59.0ms	(sqrt (+ (* re re) (* im im)))
50.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts: 76 → 76

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.3b

regimes523.0ms

Accuracy

57% (9.8b remaining)

Error of 17.2b against oracle of 7.4b and baseline of 30.2b

bsearch148.0ms

end0.0ms

sample741.0ms

Algorithm

intervals

Results

571.0ms

8000×

body

valid