Details

sample47.0ms

Algorithm

intervals

Results

24.0ms

271×

body

valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma y.re y.re (* y.im y.im))
0.5b	(fma x.re y.re (* x.im y.im))
26.1b	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite11.0ms

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

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma y.re y.re (* y.im y.im))
0.0ms	(fma x.re y.re (* x.im y.im))
9.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

series249.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(fma y.re y.re (* y.im y.im))
59.0ms	(fma x.re y.re (* x.im y.im))
136.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify2.2s

Counts

58 → 58

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	74	833
1	114	819
2	287	707
3	782	707
4	2290	707
done	5000	707

prune244.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
0.5b	(fma x.re y.re (* x.im y.im))
17.2b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite42.0ms

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:

33.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
0.0ms	(fma x.re y.re (* x.im y.im))
5.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

series471.0ms

Counts

3 → 9

Calls

3 calls:

228.0ms	(* (/ 1 (hypot y.im y.re)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)))
62.0ms	(fma x.re y.re (* x.im y.im))
181.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify3.7s

Counts

106 → 106

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	140	1895
1	328	1763
2	1068	1527
3	3979	1527
done	5000	1494

prune269.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b	(fma x.re y.re (* x.im y.im))
17.2b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

rewrite21.0ms

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

series321.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re)) (hypot y.im y.re))
46.0ms	(fma x.re y.re (* x.im y.im))
140.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.im y.re))

simplify2.1s

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

prune875.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.im y.re))) (hypot y.im y.re))
0.5b	(fma x.re y.re (* x.im y.im))
17.3b	(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.im y.re)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

28.0ms	(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.im y.re))) (hypot y.im y.re))
1.0ms	(fma x.re y.re (* x.im y.im))
20.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.im y.re)))

series429.0ms

Counts

3 → 9

Calls

3 calls:

186.0ms	(/ (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.im y.re))) (hypot y.im y.re))
51.0ms	(fma x.re y.re (* x.im y.im))
191.0ms	(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.im y.re)))

simplify4.3s

Counts

86 → 86

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	120	1355
1	267	1194
2	784	980
3	3069	966
done	5000	966

prune345.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.0b

regimes260.0ms

Accuracy

30.9% (7.8b remaining)

Error of 13.4b against oracle of 5.6b and baseline of 16.9b

bsearch77.0ms

Steps

Iters	Range		Point
4	4.564852210057707e+83	8.26536377327354e+83	8.140603411282213e+83
8	-8.514940969726654e+214	-4.9402977088155893e+210	-6.01901390366994e+211

simplify8.0ms

Iterations

Useful iterations: done (8.0ms)

Iter	Nodes	Cost
0	23	45
1	30	39
done	30	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

809.0ms

8514×

body

valid