Details

sample31.0ms

Algorithm

intervals

Results

14.0ms

264×

body

valid

simplify88.0ms

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: 28.5b

localize11.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (* x.im y.re) (* x.re y.im))
28.0b	(/ (- (* 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` `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:

9.0ms	(- (* x.im y.re) (* x.re y.im))
31.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series152.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (* x.im y.re) (* x.re y.im))
107.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.6s

Counts

56 → 56

Iterations

Useful iterations: done (1.6s)

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

prune231.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)))
0.8b	(fma x.im y.re (- (* y.im x.re)))
18.9b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite46.0ms

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.re y.im)
32.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
1.0ms	(fma x.im y.re (- (* y.im x.re)))
10.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

series560.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(hypot y.re y.im)
246.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)))
64.0ms	(fma x.im y.re (- (* y.im x.re)))
184.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify3.7s

Counts

119 → 119

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	148	2085
1	346	1952
2	1092	1694
3	4189	1694
done	5001	1660

prune554.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
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)))
18.9b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite21.0ms

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.re y.im)
11.0ms	(/ (/ (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))

series539.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot y.re y.im)
218.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (hypot y.re y.im))
63.0ms	(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))

simplify2.1s

Counts

133 → 133

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	169	2712
1	340	2650
2	752	2455
3	2558	2401
done	5002	2337

prune862.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt 1) (sqrt (hypot y.re y.im))) (/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (sqrt (hypot y.re y.im))))
0.3b	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
0.8b	(fma x.im y.re (- (* y.im x.re)))
18.9b	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

390×	`times-frac`
315×	`add-sqr-sqrt`
193×	`*-un-lft-identity`
183×	`add-cube-cbrt`
166×	`sqrt-prod`
82×	`associate-r`
40×	`associate-l`
35×	`unswap-sqr`
32×	`add-exp-log` `add-cbrt-cube`
17×	`div-inv`
16×	`associate-/l*`
13×	`cbrt-undiv` `div-exp`
9×	`associate-/r*`
6×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 336

Calls

4 calls:

128.0ms	(* (/ (sqrt 1) (sqrt (hypot y.re y.im))) (/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (sqrt (hypot y.re y.im))))
14.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (sqrt (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))

series1.1s

Counts

4 → 12

Calls

4 calls:

289.0ms	(* (/ (sqrt 1) (sqrt (hypot y.re y.im))) (/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (sqrt (hypot y.re y.im))))
567.0ms	(/ (/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
65.0ms	(fma x.im y.re (- (* y.im x.re)))
191.0ms	(/ (fma x.im y.re (- (* y.im x.re))) (hypot y.re y.im))

simplify2.1s

Counts

348 → 348

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	373	10523
1	1029	9702
2	2870	8456
done	5000	8440

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

regimes303.0ms

Accuracy

32.8% (8.1b remaining)

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

bsearch111.0ms

Steps

Iters	Range		Point
8	2.0010442062530377e+129	1.0873747118125966e+132	9.991764747534992e+131
8	-2.3729376157764536e+152	-1.769171722317776e+149	-8.623094169584485e+150

simplify19.0ms

Iterations

Useful iterations: 3 (15.0ms)

Iter	Nodes	Cost
0	26	58
1	37	46
2	40	40
3	44	34
done	44	34

end0.0ms

sample1.4s

Algorithm

intervals

Results

842.0ms

8474×

body

valid