Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

269×

body

valid

simplify66.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
27.7b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite34.0ms

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:

8.0ms	(- (* x.im y.re) (* x.re y.im))
25.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series130.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (* x.im y.re) (* x.re y.im))
92.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.3s

Counts

56 → 56

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	97	1020
1	271	919
2	930	841
3	3199	837
done	5000	836

prune156.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y.re y.im))
0.2b	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
0.3b	(fma x.im y.re (- (* y.im x.re)))
17.4b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite39.0ms

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×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

5.0ms	(/ 1 (hypot y.re y.im))
23.0ms	(* (/ 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))

series428.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (hypot y.re y.im))
187.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
47.0ms	(fma x.im y.re (- (* y.im x.re)))
140.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify2.6s

Counts

142 → 142

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	155	2322
1	358	2140
2	1094	1888
3	4124	1874
done	5001	1840

prune340.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

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))
0.3b	(fma x.im y.re (- (* y.im x.re)))
17.4b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite23.0ms

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:

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

series333.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
46.0ms	(fma x.im y.re (- (* y.im x.re)))
145.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify1.5s

Counts

120 → 120

Iterations

Useful iterations: done (1.5s)

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

prune388.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (+ (* y.re x.im) (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
0.3b	(+ (* y.re x.im) (- (* y.im x.re)))
17.4b	(/ (+ (* y.re x.im) (- (* y.im x.re))) (hypot y.re y.im))

rewrite69.0ms

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`
9×	`div-sub`
7×	`add-log-exp`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `neg-sub0` `expm1-log1p-u` `associate-+r-` `unsub-neg` `log1p-expm1-u` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+`
1×	`+-commutative` `fma-def` `neg-log`

Counts

3 → 127

Calls

3 calls:

28.0ms	(/ (/ (+ (* y.re x.im) (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms	(+ (* y.re x.im) (- (* y.im x.re)))
25.0ms	(/ (+ (* y.re x.im) (- (* y.im x.re))) (hypot y.re y.im))

series281.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(/ (/ (+ (* y.re x.im) (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
43.0ms	(+ (* y.re x.im) (- (* y.im x.re)))
112.0ms	(/ (+ (* y.re x.im) (- (* y.im x.re))) (hypot y.re y.im))

simplify1.0s

Counts

136 → 136

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	187	3058
1	441	2807
2	1265	2612
done	5000	2556

prune401.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

regimes199.0ms

Accuracy

33.1% (8.1b remaining)

Error of 12.9b against oracle of 4.8b and baseline of 16.9b

bsearch64.0ms

Steps

Iters	Range		Point
5	3.1995439014547363e+193	7.923655262303924e+193	3.313512139340002e+193
8	-4.354416350763856e+162	-3.226459196029535e+159	-2.0381197724134258e+160

simplify10.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	50
1	39	44
2	42	44
3	45	44
4	46	44
done	46	44

end0.0ms

sample585.0ms

Algorithm

intervals

Results

289.0ms

8473×

body

valid