Details

sample49.0ms

Algorithm

intervals

Results

23.0ms

274×

body

valid

simplify85.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
26.4b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite54.0ms

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

Counts

3 → 55

Calls

3 calls:

12.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
32.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series216.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (* y.re y.re) (* y.im y.im))
67.0ms	(- (* x.im y.re) (* x.re y.im))
112.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify513.0ms

Counts: 64 → 64

prune291.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.0b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite85.0ms

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

Counts

4 → 86

Calls

4 calls:

15.0ms	(- (* x.im y.re) (* x.re y.im))
41.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
10.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* x.im y.re) (* x.re y.im))
185.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
43.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts: 98 → 98

prune479.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 23.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.6b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.7b	(- (* x.im y.re) (* x.re y.im))
26.2b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `flip3-+` `associate-l` `associate-/r` `flip--` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 98

Calls

4 calls:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
14.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(- (* x.im y.re) (* x.re y.im))
59.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* y.re y.re) (* y.im y.im))
71.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
72.0ms	(- (* x.im y.re) (* x.re y.im))
121.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify798.0ms

Counts: 110 → 110

prune457.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 23.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
26.2b	(* (- (* x.im y.re) (* x.re y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
173×	`add-sqr-sqrt`
150×	`associate-r`
141×	`sqrt-prod`
138×	`*-un-lft-identity`
134×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`sqrt-div`
14×	`associate-/r/`
13×	`add-cbrt-cube`
12×	`unswap-sqr`
9×	`flip3-+` `flip-+`
8×	`pow1` `div-inv`
6×	`div-exp` `add-log-exp`
5×	`prod-exp`
3×	`cbrt-undiv` `flip3--` `associate-l` `flip--` `cbrt-unprod`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 229

Calls

4 calls:

10.0ms	(- (* x.im y.re) (* x.re y.im))
225.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
16.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* x.im y.re) (* x.re y.im))
149.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
77.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
67.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify697.0ms

Counts: 241 → 241

prune985.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 23.2b

regimes239.0ms

Accuracy

-2.5% (2.7b remaining)

Error of 26.5b against oracle of 23.8b and baseline of 26.4b

bsearch0.0ms

simplify157.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s

8506×

body

valid