Details

sample49.0ms

Algorithm

intervals

Results

23.0ms

271×

body

valid

simplify100.0ms

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: 24.7b

localize13.0ms

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))
24.2b	(/ (- (* 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:

14.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(- (* x.im y.re) (* x.re y.im))
29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series236.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ (* y.re y.re) (* y.im y.im))
59.0ms	(- (* x.im y.re) (* x.re y.im))
125.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify3.4s

Counts

64 → 64

Iterations

Useful iterations: 2 (259.0ms)

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

prune333.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 24.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (* x.im y.re) (* x.re y.im))
16.1b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite64.0ms

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:

9.0ms	(- (* x.im y.re) (* x.re y.im))
29.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* x.im y.re) (* x.re y.im))
180.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
46.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.4s

Counts

98 → 98

Iterations

Useful iterations: 3 (717.0ms)

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

prune452.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.4b

localize23.0ms

Local error

Found 4 expressions with local error:

11.1b	(/ (* x.im y.re) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
14×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-div`
7×	`pow1`
6×	`times-frac` `associate-/r*`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

36.0ms	(/ (* x.im y.re) (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)))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (* x.im y.re) (sqrt (+ (* y.re y.re) (* y.im y.im))))
66.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
64.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
71.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.8s

Counts

86 → 86

Iterations

Useful iterations: 3 (755.0ms)

Iter	Nodes	Cost
0	84	1174
1	200	1042
2	610	934
3	2296	912
done	5000	912

prune418.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.1b

localize24.0ms

Local error

Found 4 expressions with local error:

26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
15.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
45.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
60.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify3.1s

Counts

72 → 72

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	38	852
1	91	744
2	205	680
3	444	656
4	1114	656
5	3182	656
done	5001	656

prune422.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.1b

regimes269.0ms

Accuracy

0% (1.7b remaining)

Error of 24.3b against oracle of 22.6b and baseline of 24.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	56
1	20	56
done	20	56

end0.0ms

sample1.1s

Algorithm

intervals

Results

657.0ms

8497×

body

valid