Details

sample40.0ms

Algorithm

intervals

Results

22.0ms

270×

body

valid

simplify126.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	11	15
1	21	14
2	40	14
3	56	14
4	76	14
5	88	14
6	92	14
done	92	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.re y.re (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
25.4b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

1.0ms	(fma y.re y.re (* y.im y.im))
18.0ms	(- (* x.im y.re) (* x.re y.im))
38.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series280.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(fma y.re y.re (* y.im y.im))
75.0ms	(- (* x.im y.re) (* x.re y.im))
165.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify3.0s

Counts

67 → 67

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	97	1039
1	228	1011
2	761	906
3	2655	892
done	5000	886

prune277.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.2b	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
0.5b	(- (* x.im y.re) (* x.re y.im))
13.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `pow-flip` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 139

Calls

4 calls:

5.0ms	(/ 1 (hypot y.re y.im))
47.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
11.0ms	(- (* x.im y.re) (* x.re y.im))
32.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series828.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1 (hypot y.re y.im))
238.0ms	(* (/ 1 (hypot y.re y.im)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
59.0ms	(- (* x.im y.re) (* x.re y.im))
469.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify1.9s

Counts

151 → 151

Iterations

Useful iterations: 2 (346.0ms)

Iter	Nodes	Cost
0	178	2462
1	470	2264
2	1552	1997
done	5000	1997

prune414.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
13.8b	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 121

Calls

3 calls:

35.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
24.0ms	(- (* x.im y.re) (* x.re y.im))
27.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series496.0ms

Counts

3 → 9

Calls

3 calls:

209.0ms	(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
74.0ms	(- (* x.im y.re) (* x.re y.im))
213.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify2.8s

Counts

130 → 130

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	187	2814
1	445	2738
2	1244	2548
3	4472	2493
done	5000	2490

prune538.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im))
0.1b	(/ (- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im)) (hypot y.re y.im))
2.1b	(* (/ y.re (hypot y.re y.im)) x.im)
8.9b	(* (/ x.re (hypot y.re y.im)) y.im)

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
29×	`times-frac`
28×	`add-cube-cbrt` `*-un-lft-identity`
26×	`associate-l`
16×	`add-exp-log` `add-cbrt-cube`
10×	`associate-*l/`
8×	`pow1`
6×	`associate-r` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `unswap-sqr`
3×	`cbrt-undiv` `div-exp` `associate-/r` `div-inv` `associate-/l`
2×	`flip3--` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num`

Counts

4 → 120

Calls

4 calls:

28.0ms	(- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im))
38.0ms	(/ (- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im)) (hypot y.re y.im))
29.0ms	(* (/ y.re (hypot y.re y.im)) x.im)
32.0ms	(* (/ x.re (hypot y.re y.im)) y.im)

series904.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im))
397.0ms	(/ (- (* (/ y.re (hypot y.re y.im)) x.im) (* (/ x.re (hypot y.re y.im)) y.im)) (hypot y.re y.im))
158.0ms	(* (/ y.re (hypot y.re y.im)) x.im)
107.0ms	(* (/ x.re (hypot y.re y.im)) y.im)

simplify1.5s

Counts

132 → 132

Iterations

Useful iterations: 2 (433.0ms)

Iter	Nodes	Cost
0	203	2079
1	483	1982
2	1462	1825
done	5000	1825

prune527.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes217.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	13	21
1	18	19
done	18	19

end0.0ms

sample1.2s

Algorithm

intervals

Results

762.0ms

8479×

body

valid