Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	194×	body	80	valid
4.0ms	23×	body	2560	valid
2.0ms	14×	body	1280	valid
2.0ms	9×	body	5120	valid
1.0ms	9×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8
done	33	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
29.6b	(sqrt (+ (* re re) (* im im)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`pow1` `add-sqr-sqrt` `sqrt-prod`
6×	`add-cube-cbrt` `fma-def`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`pow1/2` `associate-*r/`
1×	`+-commutative` `rem-sqrt-square` `pow-prod-down` `sum-log` `hypot-def` `distribute-lft-out`

Counts

3 → 53

Calls

3 calls:

26.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
32.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series263.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify71.0ms

Counts

62 → 62

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	264	372
1	830	337
2	2660	322
3	5002	320
done	5002	320

prune178.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
0.0b	(hypot re im)
0.9b	(+ re (hypot re im))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
6×	`*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt` `associate-*r/`
3×	`add-exp-log` `expm1-log1p-u` `fma-def` `sqrt-pow1` `pow-prod-down` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3-+` `sqrt-div` `flip-+`
1×	`+-commutative` `hypot-udef` `pow1/2` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

3 → 43

Calls

3 calls:

22.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
0.0ms	(hypot re im)
6.0ms	(+ re (hypot re im))

series298.0ms

Counts

3 → 9

Calls

3 calls:

188.0ms	(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
51.0ms	(hypot re im)
59.0ms	(+ re (hypot re im))

simplify80.0ms

Counts

52 → 52

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	208	209
1	808	191
2	3269	185
3	5001	185
done	5001	185

prune148.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.0b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
15×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 97

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
12.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt (hypot re im))
86.0ms	(sqrt (hypot re im))
51.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
55.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify35.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	224	457
1	848	384
2	5001	355
done	5001	355

prune255.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.0b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))
8.0b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))
8.0b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
15×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-log-exp`
9×	`fma-def`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `pow-sqr` `flip-+`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 99

Calls

4 calls:

12.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
6.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))
6.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))
10.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
61.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))
55.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))
61.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify170.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	161	547
1	592	446
2	3637	426
3	5001	426
done	5001	426

prune345.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.3b

regimes150.0ms

Accuracy

30.2% (4.0b remaining)

Error of 11.5b against oracle of 7.5b and baseline of 13.3b

bsearch43.0ms

Steps

Iters	Range		Point
8	-1.3259787995368483e+39	-2.6306519911584922e+36	-6.300475905611319e+37

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	30	13
2	30	13
done	30	13

end0.0ms

sample674.0ms

Algorithm

intervals

Results

188.0ms	6025×	body	80	valid
119.0ms	664×	body	2560	valid
71.0ms	287×	body	5120	valid
70.0ms	492×	body	1280	valid
32.0ms	280×	body	640	valid
14.0ms	158×	body	320	valid
5.0ms	94×	body	160	valid