Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

264×

body

valid

simplify38.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	19	15
2	36	15
3	48	15
4	66	15
5	72	15
done	72	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.2b	(- (* x.im y.re) (* x.re y.im))
25.0b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite18.0ms

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:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
2.0ms	(- (* x.im y.re) (* x.re y.im))
10.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series147.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* y.re y.re) (* y.im y.im))
35.0ms	(- (* x.im y.re) (* x.re y.im))
85.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.7s

Counts

64 → 64

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	102	1120
1	289	1097
2	1023	981
3	3795	981
done	5000	980

prune186.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.8b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* x.im y.re) (* x.re y.im))
15.9b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

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:

2.0ms	(- (* x.im y.re) (* x.re y.im))
11.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* x.im y.re) (* x.re y.im))
113.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
41.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts

98 → 98

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	121	1814
1	304	1682
2	854	1574
3	2501	1558
done	5000	1557

prune297.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.0b

localize17.0ms

Local error

Found 4 expressions with local error:

14.2b	(* (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
16.5b	(cbrt (- (* x.im y.re) (* x.re y.im)))
16.5b	(cbrt (- (* x.im y.re) (* x.re y.im)))
16.5b	(cbrt (- (* x.im y.re) (* x.re y.im)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
25×	`add-sqr-sqrt`
24×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
19×	`cbrt-prod`
16×	`add-exp-log` `frac-times`
15×	`flip3--` `flip--`
12×	`associate-*l/`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+` `div-inv`

Counts

4 → 102

Calls

4 calls:

52.0ms	(* (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
2.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
2.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
2.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (* (cbrt (- (* x.im y.re) (* x.re y.im))) (cbrt (- (* x.im y.re) (* x.re y.im)))) (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
112.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
115.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
120.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))

simplify1.0s

Counts

114 → 114

Iterations

Useful iterations: 2 (312.0ms)

Iter	Nodes	Cost
0	196	3637
1	601	3519
2	1962	2956
done	5000	2956

prune393.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 23.0b

localize20.0ms

Local error

Found 4 expressions with local error:

16.5b	(cbrt (- (* x.im y.re) (* x.re y.im)))
21.6b	(cbrt (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
21.6b	(cbrt (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
21.6b	(cbrt (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

102×	`cbrt-prod`
54×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-/r/`
5×	`cbrt-div`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `div-inv`
1×	`flip3--` `flip--`

Counts

4 → 112

Calls

4 calls:

2.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
5.0ms	(cbrt (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(cbrt (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(cbrt (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))

series911.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (- (* x.im y.re) (* x.re y.im)))
270.0ms	(cbrt (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
261.0ms	(cbrt (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))
264.0ms	(cbrt (/ (cbrt (- (* x.im y.re) (* x.re y.im))) (+ (* y.re y.re) (* y.im y.im))))

simplify1.2s

Counts

124 → 124

Iterations

Useful iterations: 3 (522.0ms)

Iter	Nodes	Cost
0	196	3844
1	433	3757
2	1068	3593
3	2845	3569
done	5000	3569

prune548.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 23.0b

regimes202.0ms

Accuracy

0% (2.8b remaining)

Error of 25.7b against oracle of 22.9b and baseline of 25.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	16	25
done	16	25

end0.0ms

sample517.0ms

Algorithm

intervals

Results

304.0ms

8495×

body

valid