Details

sample30.0ms

Algorithm

intervals

Results

14.0ms

268×

body

valid

simplify101.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
1.4b	(- (* x.im y.re) (* x.re y.im))
24.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite79.0ms

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` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `sum-log` `div-inv`

Counts

3 → 64

Calls

3 calls:

14.0ms	(+ (* y.re y.re) (* y.im y.im))
14.0ms	(- (* x.im y.re) (* x.re y.im))
48.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series244.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ (* y.re y.re) (* y.im y.im))
61.0ms	(- (* x.im y.re) (* x.re y.im))
137.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.1s

Counts

73 → 73

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	112	1202
1	314	1070
2	1053	961
3	3501	961
done	5000	960

prune358.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
0.8b	(fma x.im y.re (- (* y.im x.re)))
15.6b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`add-exp-log` `*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `fma-udef`

Counts

3 → 97

Calls

3 calls:

50.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
0.0ms	(fma x.im y.re (- (* y.im x.re)))
5.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

series531.0ms

Counts

3 → 9

Calls

3 calls:

260.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
84.0ms	(fma x.im y.re (- (* y.im x.re)))
187.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify3.3s

Counts

106 → 106

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	141	2025
1	335	1894
2	1078	1642
3	4196	1642
done	5001	1608

prune359.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
0.8b	(fma x.im y.re (- (* y.im x.re)))
15.6b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite38.0ms

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`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

24.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
1.0ms	(fma x.im y.re (- (* y.im x.re)))
9.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

series522.0ms

Counts

3 → 9

Calls

3 calls:

247.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
68.0ms	(fma x.im y.re (- (* y.im x.re)))
207.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify2.3s

Counts

120 → 120

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	162	2652
1	329	2592
2	746	2403
3	2552	2349
done	5000	2285

prune539.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re))))) (hypot y.re y.im))
0.2b	(/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re)))))
0.8b	(fma x.im y.re (- (* y.im x.re)))
15.6b	(/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 319

Calls

4 calls:

39.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re))))) (hypot y.re y.im))
11.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re)))))
0.0ms	(fma x.im y.re (- (* y.im x.re)))
5.0ms	(/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(/ (/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re))))) (hypot y.re y.im))
174.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re)))))
79.0ms	(fma x.im y.re (- (* y.im x.re)))
125.0ms	(/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re))))

simplify2.1s

Counts

331 → 331

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	460	9298
1	1020	8210
2	1912	7632
done	5000	7450

prune978.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.2b

regimes379.0ms

Accuracy

35.3% (7.3b remaining)

Error of 12.6b against oracle of 5.3b and baseline of 16.6b

bsearch149.0ms

Steps

Iters	Range		Point
11	1.3202626764746345e+144	1.2662851632966894e+177	3.3678318389903335e+157
8	-7.066707918776839e+146	-1.0923850232644114e+143	-4.468015220407937e+144

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	42
1	32	36
2	34	36
done	34	36

end0.0ms

sample1.4s

Algorithm

intervals

Results

853.0ms

8530×

body

valid