Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

276×

body

valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(+ (* x.re y.re) (* x.im y.im))
28.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite49.0ms

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×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 42

Calls

2 calls:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
40.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series364.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ (* x.re y.re) (* x.im y.im))
329.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Counts: 48 → 48

prune153.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 28.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* x.re y.re) (* x.im y.im))
18.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite62.0ms

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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
36.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* x.re y.re) (* x.im y.im))
113.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
39.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify74.0ms

Counts: 96 → 96

prune285.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 25.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* x.re y.re) (* x.im y.im))
18.4b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite48.0ms

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` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
22.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* x.re y.re) (* x.im y.im))
98.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (+ (* x.re y.re) (* x.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify67.0ms

Counts: 96 → 96

prune321.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 25.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (* x.re y.re) (* x.im y.im))
18.5b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite87.0ms

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`
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` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

8.0ms	(+ (* x.re y.re) (* x.im y.im))
60.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* x.re y.re) (* x.im y.im))
117.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
42.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify46.0ms

Counts: 106 → 106

prune305.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 25.7b

regimes246.0ms

Accuracy

17.5% (2.7b remaining)

Error of 25.8b against oracle of 23.1b and baseline of 26.3b

bsearch2.0ms

simplify1.0ms

end0.0ms

sample865.0ms

Algorithm

intervals

Results

518.0ms

8489×

body

valid