Details

sample58.0ms

Algorithm

intervals

Results

39.0ms

266×

body

valid

simplify86.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	70
5	70
4	66
3	48
2	36
1	19
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.1b	(- (* x.im y.re) (* x.re y.im))
27.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/r` `insert-posit16` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

3 → 58

Calls

3 calls:

11.0ms	(+ (* y.re y.re) (* y.im y.im))
15.0ms	(- (* x.im y.re) (* x.re y.im))
43.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series201.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* y.re y.re) (* y.im y.im))
45.0ms	(- (* x.im y.re) (* x.re y.im))
119.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts

67 → 67

Iterations

Iter	Nodes
3	4729
2	1206
1	305
0	104

prune856.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 27.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
18.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite55.0ms

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`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

14.0ms	(- (* x.im y.re) (* x.re y.im))
27.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.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)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* x.im y.re) (* x.re y.im))
133.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify871.0ms

Counts

102 → 102

Iterations

Iter	Nodes
3	2589
2	934
1	315
0	124

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.2b

localize33.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
18.2b	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `associate-/l*` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r*` `flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

4 → 89

Calls

4 calls:

17.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* x.im y.re) (* x.re y.im))
127.0ms	(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify653.0ms

Counts

101 → 101

Iterations

Iter	Nodes
3	2005
2	763
1	275
0	119

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.2b

localize35.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (* x.im y.re) (* x.re y.im))
18.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite82.0ms

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`
4×	`insert-posit16`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 90

Calls

4 calls:

17.0ms	(- (* x.im y.re) (* x.re y.im))
44.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* x.im y.re) (* x.re y.im))
170.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
62.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify800.0ms

Counts

102 → 102

Iterations

Iter	Nodes
3	2589
2	934
1	315
0	124

prune1.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 25.2b

regimes596.0ms

Accuracy

0% (2.5b remaining)

Error of 25.5b against oracle of 22.9b and baseline of 25.5b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	20
1	20
0	15

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s

8452×

body

valid