Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

256×

body

valid

simplify1.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* re re) (* im im))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

9.0ms	(+ (* re re) (* im im))
10.0ms	(sqrt (+ (* re re) (* im im)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(+ (* re re) (* im im))
47.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Counts: 32 → 32

prune138.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (* re re) (* im im))))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

6.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
9.0ms	(sqrt (+ (* re re) (* im im)))
10.0ms	(sqrt (+ (* re re) (* im im)))
14.0ms	(sqrt (+ (* re re) (* im im)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (sqrt (+ (* re re) (* im im))))
60.0ms	(sqrt (+ (* re re) (* im im)))
48.0ms	(sqrt (+ (* re re) (* im im)))
61.0ms	(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Counts: 73 → 73

prune347.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.3b

localize36.0ms

Local error

Found 4 expressions with local error:

28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series217.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (+ (* re re) (* im im)))
45.0ms	(sqrt (+ (* re re) (* im im)))
56.0ms	(sqrt (+ (* re re) (* im im)))
59.0ms	(sqrt (+ (* re re) (* im im)))

simplify135.0ms

Counts: 72 → 72

prune264.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 7.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* re re) (* im im))
5.7b	(exp (log (sqrt (+ (* re re) (* im im)))))
28.5b	(sqrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

9.0ms	(+ (* re re) (* im im))
12.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
10.0ms	(sqrt (+ (* re re) (* im im)))

series116.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* re re) (* im im))
40.0ms	(exp (log (sqrt (+ (* re re) (* im im)))))
45.0ms	(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Counts: 57 → 57

prune436.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.3b

regimes389.0ms

Accuracy

58.9% (9.9b remaining)

Error of 17.7b against oracle of 7.8b and baseline of 31.9b

bsearch55.0ms

Steps

Iters	Range		Point
10	1.2073698495971617e+61	3.217811591970086e+74	2.7153468834491098e+73
5	-1.7457635943519997e+137	-5.665103565004941e+136	-1.2876568362185878e+137

simplify2.0ms

end0.0ms

sample712.0ms

Algorithm

intervals

Results

393.0ms

8000×

body

valid