Details

sample19.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify5.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize37.0ms

Local error

Found 2 expressions with local error:

26.0b	(sqrt (+ (* re re) (* im im)))
0.0b	(+ (* re re) (* im im))

rewrite27.0ms

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:

Slowest

14.0ms	(+ (* re re) (* im im))
12.0ms	(sqrt (+ (* re re) (* im im)))

series101.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

66.0ms	(sqrt (+ (* re re) (* im im)))
35.0ms	(+ (* re re) (* im im))

simplify1.6s

Counts: 34 → 34

prune311.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.4b

localize35.0ms

Local error

Found 4 expressions with local error:

26.0b	(sqrt (+ (* re re) (* im im)))
26.0b	(sqrt (+ (* re re) (* im im)))
26.0b	(sqrt (+ (* re re) (* im im)))
0.6b	(cbrt (sqrt (+ (* re re) (* im im))))

rewrite31.0ms

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

10.0ms	(sqrt (+ (* re re) (* im im)))
9.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
5.0ms	(cbrt (sqrt (+ (* re re) (* im im))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

99.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
67.0ms	(sqrt (+ (* re re) (* im im)))
53.0ms	(sqrt (+ (* re re) (* im im)))
43.0ms	(sqrt (+ (* re re) (* im im)))

simplify934.0ms

Counts: 77 → 77

prune861.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.4b

localize31.0ms

Local error

Found 4 expressions with local error:

26.0b	(sqrt (+ (* re re) (* im im)))
26.0b	(sqrt (+ (* re re) (* im im)))
26.0b	(sqrt (+ (* re re) (* im im)))
5.0b	(pow (sqrt (+ (* re re) (* im im))) 1/3)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
6×	`unpow-prod-down` `sqrt-div`
5×	`add-exp-log`
4×	`sqrt-pow1` `add-cbrt-cube` `pow1/2` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `pow-unpow` `pow-pow` `flip3-+` `flip-+`
1×	`pow-to-exp` `unpow1/3` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

Slowest

14.0ms	(pow (sqrt (+ (* re re) (* im im))) 1/3)
7.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))
6.0ms	(sqrt (+ (* re re) (* im im)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

138.0ms	(pow (sqrt (+ (* re re) (* im im))) 1/3)
55.0ms	(sqrt (+ (* re re) (* im im)))
52.0ms	(sqrt (+ (* re re) (* im im)))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts: 85 → 85

prune966.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.4b

localize60.0ms

Local error

Found 4 expressions with local error:

26.0b	(sqrt (+ (* re re) (* im im)))
26.0b	(sqrt (+ (* re re) (* im im)))
26.0b	(sqrt (+ (* re re) (* im im)))
5.2b	(pow (pow (sqrt (+ (* re re) (* im im))) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

Slowest

15.0ms	(pow (pow (sqrt (+ (* re re) (* im im))) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
13.0ms	(sqrt (+ (* re re) (* im im)))
12.0ms	(sqrt (+ (* re re) (* im im)))
10.0ms	(sqrt (+ (* re re) (* im im)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

422.0ms	(pow (pow (sqrt (+ (* re re) (* im im))) (* (cbrt 1/3) (cbrt 1/3))) (cbrt 1/3))
67.0ms	(sqrt (+ (* re re) (* im im)))
55.0ms	(sqrt (+ (* re re) (* im im)))
46.0ms	(sqrt (+ (* re re) (* im im)))

simplify769.0ms

Counts: 90 → 90

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.4b

regimes525.0ms

Accuracy

57.7% (9.4b remaining)

Error of 16.8b against oracle of 7.4b and baseline of 29.7b

bsearch65.0ms

end0.0ms

sample800.0ms

Algorithm

intervals

Results

640.0ms

8000×

body

valid