Details

sample63.0ms

Algorithm

intervals

Results

42.0ms

272×

body

valid

simplify31.0ms

Counts: 1 → 1

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize39.0ms

Local error

Found 2 expressions with local error:

25.0b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
0.2b	(+ (* x.re y.re) (* x.im y.im))

rewrite76.0ms

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

55.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(+ (* x.re y.re) (* x.im y.im))

series171.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

126.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(+ (* x.re y.re) (* x.im y.im))

simplify983.0ms

Counts: 50 → 50

prune464.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.5b

localize30.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
0.2b	(+ (* x.re y.re) (* x.im y.im))

rewrite69.0ms

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))))
7.0ms	(+ (* 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)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

160.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
63.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
54.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
37.0ms	(+ (* x.re y.re) (* x.im y.im))

simplify1.0s

Counts: 100 → 100

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 22.7b

localize30.0ms

Local error

Found 4 expressions with local error:

27.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 104

Calls

4 calls:

Slowest

46.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
11.0ms	(sqrt (+ (* y.re y.re) (* y.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)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

215.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
61.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify905.0ms

Counts: 116 → 116

prune1.6s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 22.7b

localize66.0ms

Local error

Found 4 expressions with local error:

28.8b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
28.8b	(cbrt (+ (* y.re y.re) (* y.im y.im)))
27.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
9.7b	(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
53×	`times-frac`
37×	`*-un-lft-identity`
33×	`associate-r` `add-cube-cbrt`
27×	`sqrt-prod`
26×	`add-exp-log`
18×	`cbrt-prod`
16×	`add-cbrt-cube`
13×	`associate-l`
12×	`unswap-sqr`
8×	`div-exp` `prod-exp`
7×	`pow1`
6×	`cbrt-div`
4×	`cbrt-undiv` `flip3-+` `sqrt-div` `cbrt-unprod` `flip-+` `insert-posit16` `add-log-exp`
2×	`rec-exp` `pow1/3` `1-exp` `associate-/r/` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 127

Calls

4 calls:

Slowest

57.0ms	(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
8.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series897.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

602.0ms	(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
146.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
108.0ms	(cbrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts: 139 → 139

prune2.5s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 22.7b

regimes667.0ms

Accuracy

0% (2.4b remaining)

Error of 26.0b against oracle of 23.6b and baseline of 26.0b

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.3s

8485×

body

valid