Details

sample49.0ms

Algorithm

intervals

Results

23.0ms

271×

body

valid

simplify68.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize21.0ms

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))
23.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite79.0ms

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:

16.0ms	(+ (* y.re y.re) (* y.im y.im))
15.0ms	(- (* x.im y.re) (* x.re y.im))
46.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series185.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* y.re y.re) (* y.im y.im))
44.0ms	(- (* x.im y.re) (* x.re y.im))
107.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify690.0ms

Counts: 64 → 64

prune276.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
14.3b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite124.0ms

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:

16.0ms	(- (* x.im y.re) (* x.re y.im))
57.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
18.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* x.im y.re) (* x.re y.im))
181.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
55.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
74.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts: 98 → 98

prune464.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.7b	(- (* x.im y.re) (* x.re y.im))
0.9b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
23.1b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite131.0ms

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:

11.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
19.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
88.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* y.re y.re) (* y.im y.im))
59.0ms	(- (* x.im y.re) (* x.re y.im))
57.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
114.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify972.0ms

Counts: 110 → 110

prune430.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.7b

localize28.0ms

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))
23.5b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite62.0ms

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:

8.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
45.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series212.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
49.0ms	(- (* x.im y.re) (* x.re y.im))
134.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify548.0ms

Counts: 64 → 64

prune218.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 20.7b

regimes223.0ms

Accuracy

21.2% (2.3b remaining)

Error of 25.2b against oracle of 22.9b and baseline of 25.8b

bsearch2.0ms

simplify124.0ms

end0.0ms

sample1.0s

Algorithm

intervals

Results

620.0ms

8435×

body

valid