Details

sample25.0ms

Algorithm

intervals

Results

9.0ms

352×

body

valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (* x.re y.im) (* x.im y.re))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 11

Calls

1 calls:

9.0ms

(+ (* x.re y.im) (* x.im y.re))

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

(+ (* x.re y.im) (* x.im y.re))

simplify123.0ms

Counts: 14 → 14

prune44.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* x.re y.im) (* x.im y.re))) (cbrt (+ (* x.re y.im) (* x.im y.re))))
0.9b	(cbrt (+ (* x.re y.im) (* x.im y.re)))
0.9b	(cbrt (+ (* x.re y.im) (* x.im y.re)))
0.9b	(cbrt (+ (* x.re y.im) (* x.im y.re)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

48.0ms	(* (cbrt (+ (* x.re y.im) (* x.im y.re))) (cbrt (+ (* x.re y.im) (* x.im y.re))))
10.0ms	(cbrt (+ (* x.re y.im) (* x.im y.re)))
5.0ms	(cbrt (+ (* x.re y.im) (* x.im y.re)))
6.0ms	(cbrt (+ (* x.re y.im) (* x.im y.re)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (cbrt (+ (* x.re y.im) (* x.im y.re))) (cbrt (+ (* x.re y.im) (* x.im y.re))))
116.0ms	(cbrt (+ (* x.re y.im) (* x.im y.re)))
123.0ms	(cbrt (+ (* x.re y.im) (* x.im y.re)))
119.0ms	(cbrt (+ (* x.re y.im) (* x.im y.re)))

simplify95.0ms

Counts: 99 → 99

prune262.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x.re y.im) (* x.im y.re))
0.3b	(sqrt (+ (* x.re y.im) (* x.im y.re)))
0.3b	(sqrt (+ (* x.re y.im) (* x.im y.re)))
0.3b	(* (sqrt (+ (* x.re y.im) (* x.im y.re))) (sqrt (+ (* x.re y.im) (* x.im y.re))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
16×	`sqrt-div`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 98

Calls

4 calls:

12.0ms	(+ (* x.re y.im) (* x.im y.re))
9.0ms	(sqrt (+ (* x.re y.im) (* x.im y.re)))
9.0ms	(sqrt (+ (* x.re y.im) (* x.im y.re)))
55.0ms	(* (sqrt (+ (* x.re y.im) (* x.im y.re))) (sqrt (+ (* x.re y.im) (* x.im y.re))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* x.re y.im) (* x.im y.re))
75.0ms	(sqrt (+ (* x.re y.im) (* x.im y.re)))
78.0ms	(sqrt (+ (* x.re y.im) (* x.im y.re)))
35.0ms	(* (sqrt (+ (* x.re y.im) (* x.im y.re))) (sqrt (+ (* x.re y.im) (* x.im y.re))))

simplify42.0ms

Counts: 110 → 110

prune208.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (fabs (cbrt (+ (* x.re y.im) (* x.im y.re)))) (sqrt (+ (* x.re y.im) (* x.im y.re)))) (sqrt (cbrt (+ (* x.re y.im) (* x.im y.re)))))
0.3b	(sqrt (+ (* x.re y.im) (* x.im y.re)))
0.9b	(cbrt (+ (* x.re y.im) (* x.im y.re)))
0.9b	(cbrt (+ (* x.re y.im) (* x.im y.re)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

14×	`sqrt-div`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod` `flip3-+` `associate-r` `sqrt-prod` `add-cbrt-cube` `flip-+`
8×	`associate-*r/`
4×	`frac-times` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow1/3` `associate-*l/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 73

Calls

4 calls:

77.0ms	(* (* (fabs (cbrt (+ (* x.re y.im) (* x.im y.re)))) (sqrt (+ (* x.re y.im) (* x.im y.re)))) (sqrt (cbrt (+ (* x.re y.im) (* x.im y.re)))))
9.0ms	(sqrt (+ (* x.re y.im) (* x.im y.re)))
5.0ms	(cbrt (+ (* x.re y.im) (* x.im y.re)))
6.0ms	(cbrt (+ (* x.re y.im) (* x.im y.re)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (* (fabs (cbrt (+ (* x.re y.im) (* x.im y.re)))) (sqrt (+ (* x.re y.im) (* x.im y.re)))) (sqrt (cbrt (+ (* x.re y.im) (* x.im y.re)))))
80.0ms	(sqrt (+ (* x.re y.im) (* x.im y.re)))
116.0ms	(cbrt (+ (* x.re y.im) (* x.im y.re)))
116.0ms	(cbrt (+ (* x.re y.im) (* x.im y.re)))

simplify52.0ms

Counts: 85 → 85

prune304.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes166.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Algorithm

intervals

Results

290.0ms

10551×

body

valid