Details

sample35.0ms

Algorithm

intervals

Results

15.0ms

280×

body

valid

simplify73.0ms

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: 25.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(- (* x.im y.re) (* x.re y.im))
24.8b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

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:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
8.0ms	(- (* x.im y.re) (* x.re y.im))
26.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series156.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* y.re y.re) (* y.im y.im))
38.0ms	(- (* x.im y.re) (* x.re y.im))
89.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts

73 → 73

Iterations

Useful iterations: done (1.5s)

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

prune200.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize11.0ms

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)))
0.3b	(fma x.im y.re (- (* y.im x.re)))
15.1b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite33.0ms

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:

25.0ms	(* (/ 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))

series384.0ms

Counts

3 → 9

Calls

3 calls:

190.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
50.0ms	(fma x.im y.re (- (* y.im x.re)))
144.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify2.6s

Counts

106 → 106

Iterations

Useful iterations: done (2.6s)

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

prune265.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.3b

localize10.0ms

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)))
15.1b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite19.0ms

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:

10.0ms	(/ (/ (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))

series330.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
50.0ms	(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))

simplify1.6s

Counts

120 → 120

Iterations

Useful iterations: done (1.6s)

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

prune336.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re)))))
0.3b	(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re))))))
0.3b	(fma x.im y.re (- (* y.im x.re)))
15.1b	(/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

187×	`times-frac`
143×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
100×	`add-exp-log`
96×	`add-cube-cbrt`
50×	`div-exp`
44×	`associate-r`
32×	`add-cbrt-cube`
28×	`prod-exp`
17×	`rec-exp` `1-exp`
16×	`associate-/r*`
15×	`unswap-sqr`
13×	`cbrt-undiv` `associate-l`
11×	`div-inv`
9×	`pow1`
6×	`cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `pow-prod-down` `inv-pow`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `associate-r/` `associate-l/` `un-div-inv` `*-commutative` `fma-udef`

Counts

4 → 240

Calls

4 calls:

9.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re)))))
43.0ms	(* (/ 1 (hypot y.re y.im)) (/ 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))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re)))))
188.0ms	(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re))))))
49.0ms	(fma x.im y.re (- (* y.im x.re)))
102.0ms	(/ (hypot y.re y.im) (fma x.im y.re (- (* y.im x.re))))

simplify2.8s

Counts

252 → 252

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	293	5682
1	729	5007
2	1541	4342
3	4439	4324
done	5000	4246

prune503.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.3b

regimes217.0ms

Accuracy

31.9% (7.9b remaining)

Error of 13.2b against oracle of 5.3b and baseline of 16.9b

bsearch59.0ms

Steps

Iters	Range		Point
6	3.0458708391958014e+68	1.5303859857698357e+69	1.5144682182949202e+69
9	-1.5363030971934703e+144	-2.4882870722039588e+138	-8.156571467291585e+143

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample559.0ms

Algorithm

intervals

Results

272.0ms

8467×

body

valid