Details

sample64.0ms

Algorithm

intervals

Results

42.0ms

273×

body

valid

simplify16.0ms

Counts: 1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize30.0ms

Local error

Found 2 expressions with local error:

24.8b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
0.4b	(+ (* x.re y.re) (* x.im y.im))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r` `flip3-+` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `insert-posit16` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

2 → 44

Calls

2 calls:

Slowest

35.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(+ (* x.re y.re) (* x.im y.im))

series127.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

91.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(+ (* x.re y.re) (* x.im y.im))

simplify806.0ms

Counts: 50 → 50

prune580.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.4b

localize63.0ms

Local error

Found 4 expressions with local error:

28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
0.4b	(+ (* x.re y.re) (* x.im y.im))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`insert-posit16`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

Slowest

33.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
11.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

114.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms	(+ (* x.re y.re) (* x.im y.im))

simplify926.0ms

Counts: 100 → 100

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.7b

localize45.0ms

Local error

Found 4 expressions with local error:

28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.8b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
0.4b	(+ (* x.re y.re) (* x.im y.im))

rewrite83.0ms

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×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp` `insert-posit16`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `sum-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 98

Calls

4 calls:

Slowest

51.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (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)))
7.0ms	(+ (* x.re y.re) (* x.im y.im))

series275.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms	(+ (* x.re y.re) (* x.im y.im))

simplify2.0s

Counts: 110 → 110

prune1.7s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.7b

localize50.0ms

Local error

Found 4 expressions with local error:

28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
0.4b	(+ (* x.re y.re) (* x.im y.im))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `sqrt-div` `add-exp-log` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`insert-posit16`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

Slowest

31.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
20.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
61.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
59.0ms	(+ (* x.re y.re) (* x.im y.im))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify940.0ms

Counts: 100 → 100

prune1.4s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.7b

regimes731.0ms

Accuracy

4.2% (2.5b remaining)

Error of 25.1b against oracle of 22.6b and baseline of 25.2b

bsearch85.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.5s

8498×

body

valid