Details

sample37.0ms

Algorithm

intervals

Results

17.0ms

271×

body

valid

simplify5.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
26.6b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 44

Calls

2 calls:

11.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series193.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (* x.im y.re) (* x.re y.im))
133.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify76.0ms

Counts: 50 → 50

prune197.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
17.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

14.0ms	(- (* x.im y.re) (* x.re y.im))
45.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* x.im y.re) (* x.re y.im))
143.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
48.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
63.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify98.0ms

Counts: 98 → 98

prune435.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 23.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
17.2b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

13.0ms	(- (* x.im y.re) (* x.re y.im))
69.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* x.im y.re) (* x.re y.im))
138.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify43.0ms

Counts: 107 → 107

prune406.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 23.4b

localize23.0ms

Local error

Found 4 expressions with local error:

17.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.8b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.8b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
29.8b	(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`sqrt-prod`
6×	`add-exp-log` `cbrt-prod` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`cbrt-div` `flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 85

Calls

4 calls:

27.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
19.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
144.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
139.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify66.0ms

Counts: 97 → 97

prune563.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.4b

regimes221.0ms

Accuracy

-2.9% (2.9b remaining)

Error of 26.2b against oracle of 23.3b and baseline of 26.2b

bsearch113.0ms

Steps

Iters	Range		Point
6	7.634858387370288e+142	4.3868455552093375e+143	4.152810026092195e+143
9	6.815249310581322e+103	4.491388250328966e+108	4.454667910693685e+108

simplify37.0ms

end0.0ms

sample1.1s

Algorithm

intervals

Results

654.0ms

8483×

body

valid