Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

268×

body

valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7
done	94	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x.im y.re) (* x.re y.im))
24.6b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

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)))

series130.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (* x.im y.re) (* x.re y.im))
91.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify101.0ms

Counts

56 → 56

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	270	481
1	1012	432
2	3842	422
3	5001	421
done	5001	421

prune156.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(- (* x.im y.re) (* x.re y.im))
0.2b	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
14.5b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-exp-log`
32×	`prod-exp`
27×	`add-cbrt-cube`
26×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
21×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`pow1` `rec-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `hypot-udef` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 120

Calls

4 calls:

0.0ms	(hypot y.re y.im)
8.0ms	(- (* x.im y.re) (* x.re y.im))
52.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
18.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series601.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot y.re y.im)
38.0ms	(- (* x.im y.re) (* x.re y.im))
395.0ms	(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
120.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify56.0ms

Counts

132 → 132

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	546	1122
1	2249	931
2	5002	929
done	5002	929

prune288.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(- (* x.im y.re) (* x.re y.im))
0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
14.5b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `hypot-udef` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 131

Calls

4 calls:

0.0ms	(hypot y.re y.im)
8.0ms	(- (* x.im y.re) (* x.re y.im))
18.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
21.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series338.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(hypot y.re y.im)
39.0ms	(- (* x.im y.re) (* x.re y.im))
125.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
122.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify50.0ms

Counts

143 → 143

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	460	1435
1	1669	1331
2	5001	1322
done	5001	1322

prune399.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (sqrt (hypot y.re y.im)))
0.3b	(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))))
6.4b	(/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
8.3b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

5792×	`times-frac`
2471×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1329×	`sqrt-prod`
172×	`div-inv`
105×	`associate-/r*`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube`
31×	`associate-/l*`
25×	`associate-/r/`
20×	`cbrt-undiv`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `associate-/l/`
1×	`flip3--` `sqrt-pow1` `pow1/2` `div-sub` `flip--` `inv-pow`

Counts

4 → 1886

Calls

4 calls:

7.0ms	(/ 1 (sqrt (hypot y.re y.im)))
68.0ms	(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))))
20.0ms	(/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
20.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ 1 (sqrt (hypot y.re y.im)))
190.0ms	(/ (/ 1 (sqrt (hypot y.re y.im))) (/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))))
171.0ms	(/ (hypot y.re y.im) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im))))
212.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (hypot y.re y.im)))

simplify429.0ms

Counts

1898 → 1898

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5002	52724
done	5002	52724

prune6.1s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 4.5b

regimes269.0ms

Accuracy

29.4% (9.0b remaining)

Error of 13.7b against oracle of 4.7b and baseline of 17.4b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	34
1	35	34
done	35	34

end0.0ms

sample574.0ms

Algorithm

intervals

Results

282.0ms

8478×

body

valid