Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

271×

body

valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.8b	(+ (* x.re y.re) (* x.im y.im))
23.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite75.0ms

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

Counts

3 → 61

Calls

3 calls:

14.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(+ (* x.re y.re) (* x.im y.im))
50.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (* y.re y.re) (* y.im y.im))
48.0ms	(+ (* x.re y.re) (* x.im y.im))
111.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify2.2s

Counts

70 → 70

Iterations

Useful iterations: 2 (285.0ms)

Iter	Nodes	Cost
0	105	1154
1	288	969
2	955	867
3	2981	867
done	5001	867

prune275.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

localize12.0ms

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.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.5b	(fma x.re y.re (* x.im y.im))
13.7b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite84.0ms

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:

12.0ms	(/ 1 (hypot y.re y.im))
49.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
1.0ms	(fma x.re y.re (* x.im y.im))
14.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series586.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1 (hypot y.re y.im))
271.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
61.0ms	(fma x.re y.re (* x.im y.im))
189.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify3.7s

Counts

142 → 142

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	154	2192
1	351	2009
2	1089	1759
3	3952	1759
done	5000	1726

prune590.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.5b	(fma x.re y.re (* x.im y.im))
13.7b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite22.0ms

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:

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

series370.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
52.0ms	(fma x.re y.re (* x.im y.im))
144.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify2.2s

Counts

120 → 120

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	161	2484
1	322	2423
2	703	2246
3	2030	2192
done	5000	2130

prune488.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
0.2b	(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
0.5b	(fma x.re y.re (* x.im y.im))
13.8b	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite89.0ms

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:

11.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
57.0ms	(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
0.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series627.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
259.0ms	(* (/ 1 (hypot y.re y.im)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
51.0ms	(fma x.re y.re (* x.im y.im))
119.0ms	(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify4.1s

Counts

252 → 252

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	292	5363
1	722	4687
2	1535	4048
3	4311	4030
done	5001	3953

prune888.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.9b

regimes360.0ms

Accuracy

39% (6.8b remaining)

Error of 12.9b against oracle of 6.0b and baseline of 17.2b

bsearch126.0ms

Steps

Iters	Range		Point
6	5.4068805428593804e+166	7.208568163524586e+167	1.4718796069697552e+167
7	-6.100795518743097e+143	-1.2728136642635444e+142	-6.168252273035428e+142

simplify8.0ms

Iterations

Useful iterations: done (8.0ms)

Iter	Nodes	Cost
0	24	48
1	31	39
done	31	33

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s

8458×

body

valid