Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

264×

body

valid

simplify52.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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: 25.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.re y.re (* y.im y.im))
1.2b	(- (* x.im y.re) (* x.re y.im))
25.0b	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

rewrite12.0ms

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:

0.0ms	(fma y.re y.re (* y.im y.im))
3.0ms	(- (* x.im y.re) (* x.re y.im))
7.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(fma y.re y.re (* y.im y.im))
37.0ms	(- (* x.im y.re) (* x.re y.im))
89.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (fma y.re y.re (* y.im y.im)))

simplify1.0s

Counts

67 → 67

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	97	1039
1	224	1011
2	745	892
3	2697	892
done	5000	890

prune193.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.2b	(* (/ 1 (hypot y.im y.re)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)))
0.3b	(fma x.im y.re (- (* y.im x.re)))
15.9b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

0.0ms	(hypot y.im y.re)
14.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)))
0.0ms	(fma x.im y.re (- (* y.im x.re)))
2.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

series433.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(hypot y.im y.re)
191.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)))
49.0ms	(fma x.im y.re (- (* y.im x.re)))
137.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

simplify3.2s

Counts

119 → 119

Iterations

Useful iterations: 2 (152.0ms)

Iter	Nodes	Cost
0	148	2085
1	366	1952
2	1088	1694
3	4778	1694
done	5000	1694

prune361.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.im y.re)
0.1b	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)) (hypot y.im y.re))
0.3b	(fma x.im y.re (- (* y.im x.re)))
15.9b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

rewrite14.0ms

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot y.im y.re)
6.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)) (hypot y.im y.re))
0.0ms	(fma x.im y.re (- (* y.im x.re)))
2.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

series390.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot y.im y.re)
147.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re)) (hypot y.im y.re))
47.0ms	(fma x.im y.re (- (* y.im x.re)))
147.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.im y.re))

simplify1.7s

Counts

133 → 133

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	169	2712
1	345	2650
2	834	2455
3	2667	2401
done	5001	2399

prune412.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))) (hypot y.im y.re))
0.2b	(/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re)))))
0.3b	(fma x.im y.re (- (* y.im x.re)))
16.0b	(/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))

rewrite48.0ms

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:

17.0ms	(/ (/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))) (hypot y.im y.re))
5.0ms	(/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re)))))
0.0ms	(fma x.im y.re (- (* y.im x.re)))
2.0ms	(/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))

series508.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))) (hypot y.im y.re))
171.0ms	(/ 1 (/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re)))))
46.0ms	(fma x.im y.re (- (* y.im x.re)))
100.0ms	(/ (hypot y.im y.re) (fma x.im y.re (- (* y.im x.re))))

simplify1.4s

Counts

331 → 331

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	459	9296
1	1079	8209
2	2185	7631
done	5001	7559

prune609.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.9b

regimes214.0ms

Accuracy

28.7% (10.0b remaining)

Error of 12.5b against oracle of 2.5b and baseline of 16.5b

bsearch81.0ms

Steps

Iters	Range		Point
6	2.364246562673592e+136	1.4357828132925017e+137	2.5019882417216274e+136
10	-1.4584171055257321e+175	-1.1045029026290381e+161	-5.9876509466672635e+162

simplify6.0ms

Iterations

Useful iterations: 2 (3.0ms)

Iter	Nodes	Cost
0	25	48
1	36	42
2	39	36
3	42	36
done	42	36

end0.0ms

sample524.0ms

Algorithm

intervals

Results

306.0ms

8495×

body

valid