Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

264×

body

valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize9.0ms

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))
26.5b	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

rewrite4.0ms

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))
2.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(fma y.re y.re (* y.im y.im))
39.0ms	(fma x.re y.re (* x.im y.im))
88.0ms	(/ (fma x.re y.re (* x.im y.im)) (fma y.re y.re (* y.im y.im)))

simplify782.0ms

Counts

58 → 58

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	74	833
1	112	819
2	320	707
3	1307	707
done	5000	707

prune174.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.0b

localize10.0ms

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.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.5b	(fma x.re y.re (* x.im y.im))
17.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

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

series386.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot y.re y.im)
181.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
37.0ms	(fma x.re y.re (* x.im y.im))
116.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify2.5s

Counts

119 → 119

Iterations

Useful iterations: 2 (147.0ms)

Iter	Nodes	Cost
0	147	1955
1	361	1821
2	1118	1579
3	4936	1579
done	5000	1579

prune331.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot y.re y.im)
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))
17.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite13.0ms

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

series323.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot y.re y.im)
118.0ms	(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (hypot y.re y.im))
42.0ms	(fma x.re y.re (* x.im y.im))
118.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify1.4s

Counts

133 → 133

Iterations

Useful iterations: 3 (519.0ms)

Iter	Nodes	Cost
0	168	2544
1	339	2481
2	876	2298
3	2764	2244
done	5001	2244

prune419.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize11.0ms

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.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.5b	(fma x.re y.re (* x.im y.im))
17.5b	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

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

series384.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot y.re y.im)
183.0ms	(* (/ 1 (hypot y.re y.im)) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
42.0ms	(fma x.re y.re (* x.im y.im))
114.0ms	(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify2.8s

Counts

119 → 119

Iterations

Useful iterations: 2 (143.0ms)

Iter	Nodes	Cost
0	147	1955
1	361	1821
2	1118	1579
3	4936	1579
done	5000	1579

prune308.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.8b

regimes209.0ms

Accuracy

37.8% (7.2b remaining)

Error of 13.1b against oracle of 5.9b and baseline of 17.4b

bsearch95.0ms

Steps

Iters	Range		Point
11	5.286434132095145e+107	2.6900018818139096e+129	1.8955542797321017e+121
10	-3.4896836630642546e+148	-1.4395777107888637e+138	-6.751507617690198e+142

simplify5.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	23	41
1	29	35
done	29	35

end0.0ms

sample509.0ms

Algorithm

intervals

Results

291.0ms

8511×

body

valid