Details

sample31.0ms

Algorithm

intervals

Results

15.0ms

272×

body

valid

simplify81.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	19	15
2	36	15
3	48	15
4	66	15
5	70	15
done	70	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize12.0ms

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))
27.2b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite52.0ms

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))
35.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series172.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* y.re y.re) (* y.im y.im))
42.0ms	(- (* x.im y.re) (* x.re y.im))
99.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.2s

Counts

64 → 64

Iterations

Useful iterations: 2 (143.0ms)

Iter	Nodes	Cost
0	102	1120
1	290	1097
2	959	981
3	3121	981
done	5001	981

prune217.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 26.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite95.0ms

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:

13.0ms	(- (* x.im y.re) (* x.re y.im))
51.0ms	(/ (- (* 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)))
13.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* x.im y.re) (* x.re y.im))
173.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
60.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.5s

Counts

98 → 98

Iterations

Useful iterations: 3 (741.0ms)

Iter	Nodes	Cost
0	121	1814
1	306	1682
2	888	1574
3	2539	1558
done	5001	1558

prune484.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 24.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.7b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite180.0ms

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×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 95

Calls

4 calls:

17.0ms	(- (* x.im y.re) (* x.re y.im))
125.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (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)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* x.im y.re) (* x.re y.im))
188.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
73.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.9s

Counts

107 → 107

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	148	1896
1	371	1651
2	1056	1483
3	3800	1467
done	5000	1467

prune436.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite119.0ms

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))
68.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
17.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* x.im y.re) (* x.re y.im))
174.0ms	(/ (- (* 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)))
57.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.4s

Counts

98 → 98

Iterations

Useful iterations: 3 (732.0ms)

Iter	Nodes	Cost
0	121	1814
1	306	1682
2	888	1574
3	2539	1558
done	5001	1558

prune446.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 24.2b

regimes290.0ms

Accuracy

0% (3.1b remaining)

Error of 25.9b against oracle of 22.8b and baseline of 25.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	21	27
done	21	27

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s

8480×

body

valid