Details

sample42.0ms

Algorithm

intervals

Results

27.0ms

275×

body

valid

simplify14.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize34.0ms

Local error

Found 2 expressions with local error:

24.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
0.8b	(+ (* x.re y.re) (* x.im y.im))

rewrite73.0ms

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

63.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(+ (* x.re y.re) (* x.im y.im))

series131.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

94.0ms	(/ (+ (* 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))

simplify938.0ms

Counts: 50 → 50

prune529.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 23.8b

localize40.0ms

Local error

Found 4 expressions with local error:

31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
0.8b	(+ (* x.re y.re) (* x.im y.im))

rewrite72.0ms

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

47.0ms	(/ (+ (* 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))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

118.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
56.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
50.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(+ (* x.re y.re) (* x.im y.im))

simplify929.0ms

Counts: 100 → 100

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.7b

localize30.0ms

Local error

Found 4 expressions with local error:

31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
0.8b	(+ (* x.re y.re) (* x.im y.im))

rewrite68.0ms

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

46.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
8.0ms	(+ (* x.re y.re) (* x.im y.im))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

120.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.0ms	(+ (* x.re y.re) (* x.im y.im))

simplify1.7s

Counts: 110 → 110

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.7b

localize23.0ms

Local error

Found 3 expressions with local error:

23.9b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))
0.8b	(+ (* x.re y.re) (* x.im y.im))
0.5b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`flip3-+` `flip-+` `add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-/r` `associate-l` `insert-posit16` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

3 → 89

Calls

3 calls:

Slowest

63.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))
19.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(+ (* x.re y.re) (* x.im y.im))

series192.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

100.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))
50.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(+ (* x.re y.re) (* x.im y.im))

simplify1.7s

Counts: 98 → 98

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 22.7b

regimes355.0ms

Accuracy

0% (2.8b remaining)

Error of 25.6b against oracle of 22.8b and baseline of 25.6b

bsearch3.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s

8497×

body

valid