Details

sample51.0ms

Algorithm

intervals

Results

23.0ms

271×

body

valid

simplify27.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.2b	(+ (* x.re y.re) (* x.im y.im))
24.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

16.0ms	(+ (* y.re y.re) (* y.im y.im))
13.0ms	(+ (* x.re y.re) (* x.im y.im))
41.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (* y.re y.re) (* y.im y.im))
42.0ms	(+ (* x.re y.re) (* x.im y.im))
123.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.0s

Counts: 62 → 62

prune319.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.0b

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
15.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite120.0ms

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:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
75.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (* x.re y.re) (* x.im y.im))
192.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
56.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts: 96 → 96

prune451.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.8b

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
15.8b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
26.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite127.0ms

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:

19.0ms	(+ (* x.re y.re) (* x.im y.im))
75.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
18.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* x.re y.re) (* x.im y.im))
178.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
53.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify963.0ms

Counts: 106 → 106

prune869.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 21.8b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
15.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite80.0ms

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:

15.0ms	(+ (* x.re y.re) (* x.im y.im))
47.0ms	(/ (+ (* 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)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* x.re y.re) (* x.im y.im))
123.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
58.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
64.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts: 96 → 96

prune389.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 21.8b

regimes298.0ms

Accuracy

25% (2.2b remaining)

Error of 25.2b against oracle of 23.1b and baseline of 26.0b

bsearch3.0ms

simplify4.3s

end0.0ms

sample1.2s

Algorithm

intervals

Results

720.0ms

8494×

body

valid