Details

sample37.0ms

Algorithm

intervals

Results

17.0ms

265×

body

valid

simplify70.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	11	15
1	21	14
2	40	14
3	56	14
4	76	14
5	90	14
6	94	14
done	94	14

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x.im y.re) (* x.re y.im))
23.4b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

13.0ms	(- (* x.im y.re) (* x.re y.im))
27.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series172.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (* x.im y.re) (* x.re y.im))
128.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify899.0ms

Counts

56 → 56

Iterations

Useful iterations: done (897.0ms)

Iter	Nodes	Cost
0	97	1020
1	278	919
2	1224	843
done	5000	841

prune411.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x.im y.re (- (* y.im x.re)))
0.0b	(/ 1 (hypot y.re y.im))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
16.1b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite45.0ms

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` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

0.0ms	(fma x.im y.re (- (* y.im x.re)))
4.0ms	(/ 1 (hypot y.re y.im))
28.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
4.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

series570.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma x.im y.re (- (* y.im x.re)))
66.0ms	(/ 1 (hypot y.re y.im))
243.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
186.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify2.4s

Counts

142 → 142

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	155	2322
1	411	2214
2	2983	1892
done	5001	1874

prune722.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
0.0b	(fma x.im y.re (- (* y.im x.re)))
0.0b	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
16.1b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot y.re y.im)
1.0ms	(fma x.im y.re (- (* y.im x.re)))
13.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
5.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

series548.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(hypot y.re y.im)
69.0ms	(fma x.im y.re (- (* y.im x.re)))
175.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
224.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify821.0ms

Counts

133 → 133

Iterations

Useful iterations: done (813.0ms)

Iter	Nodes	Cost
0	169	2712
1	369	2650
2	1776	2463
done	5000	2413

prune873.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x.im y.re (- (* y.im x.re)))
0.0b	(/ 1 (hypot y.re y.im))
0.0b	(/ (* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
16.2b	(* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

1.0ms	(fma x.im y.re (- (* y.im x.re)))
7.0ms	(/ 1 (hypot y.re y.im))
11.0ms	(/ (* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
18.0ms	(* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(fma x.im y.re (- (* y.im x.re)))
75.0ms	(/ 1 (hypot y.re y.im))
184.0ms	(/ (* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im))) (hypot y.re y.im))
205.0ms	(* (fma x.im y.re (- (* y.im x.re))) (/ 1 (hypot y.re y.im)))

simplify1.3s

Counts

122 → 122

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	134	1746
1	313	1541
2	2164	1309
done	5001	1301

prune615.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.4b

regimes583.0ms

Accuracy

35.7% (7.2b remaining)

Error of 13.0b against oracle of 5.8b and baseline of 17.0b

bsearch119.0ms

Steps

Iters	Range		Point
10	1.1482141173686816e+66	1.003350963699018e+79	8.633440364875592e+78
9	-1.4819599476454846e+147	-2.1242108090092025e+141	-1.1022615428664649e+147

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	34
1	25	34
2	27	34
done	27	34

end0.0ms

sample1.3s

Algorithm

intervals

Results

793.0ms

8456×

body

valid