Details

sample28.0ms

Algorithm

intervals

Results

6.0ms	185×	body	80	valid
5.0ms	29×	body	2560	valid
3.0ms	14×	body	5120	valid
2.0ms	16×	body	1280	valid
1.0ms	6×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	8
1	28	8
2	36	8
3	44	8
4	46	8
5	46	8
done	46	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.4b	(- (sqrt (+ (* re re) (* im im))) re)
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `prod-diff`
17×	`sqrt-prod`
7×	`pow1`
6×	`fma-neg`
5×	`add-log-exp`
4×	`sqrt-div`
3×	`add-exp-log` `expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `pow1/2` `associate-*r/` `flip--` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `flip3-+` `diff-log` `pow-prod-down` `flip-+` `hypot-def` `distribute-lft-out--`

Counts

3 → 74

Calls

3 calls:

55.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
50.0ms	(- (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
49.0ms	(- (sqrt (+ (* re re) (* im im))) re)
37.0ms	(sqrt (+ (* re re) (* im im)))

simplify42.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	314	760
1	1192	522
2	5001	473
done	5001	473

prune187.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 8.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.0b	(hypot re im)
0.4b	(- (hypot re im) re)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`add-log-exp`
3×	`add-exp-log` `expm1-log1p-u` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`sub-neg` `hypot-udef` `flip3--` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 53

Calls

3 calls:

23.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
0.0ms	(hypot re im)
7.0ms	(- (hypot re im) re)

series283.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(sqrt (* 2.0 (+ (- (hypot re im) re) 0)))
48.0ms	(hypot re im)
56.0ms	(- (hypot re im) re)

simplify46.0ms

Counts

62 → 62

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	283	345
1	1118	247
2	5001	236
done	5001	236

prune152.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0))))
0.4b	(* (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))) (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
0.4b	(- (hypot re im) re)
0.4b	(- (hypot re im) re)

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-pow1`
65×	`pow1`
44×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `sqrt-prod`
28×	`sqrt-div`
27×	`add-cube-cbrt`
23×	`pow-prod-down`
20×	`pow1/2`
18×	`prod-diff`
16×	`associate-*r/`
14×	`pow-prod-up`
9×	`swap-sqr`
8×	`pow-sqr` `add-log-exp`
7×	`flip3-+` `associate-r` `associate-l` `flip-+`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
2×	`sub-neg` `flip3--` `diff-log` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

21.0ms	(sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0))))
160.0ms	(* (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))) (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
6.0ms	(- (hypot re im) re)
7.0ms	(- (hypot re im) re)

series526.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0))))
181.0ms	(* (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))) (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
60.0ms	(- (hypot re im) re)
61.0ms	(- (hypot re im) re)

simplify84.0ms

Counts

170 → 170

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	486	1300
1	2225	1060
2	5001	1032
done	5001	1032

prune401.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
0.4b	(cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
0.4b	(cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
0.7b	(pow (cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0))))) 4)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
20×	`sqrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-div`
10×	`unpow-prod-down`
6×	`cbrt-div` `associate-*r/`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

22.0ms	(cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
22.0ms	(cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
24.0ms	(cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
8.0ms	(pow (cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0))))) 4)

series1.4s

Counts

4 → 12

Calls

4 calls:

314.0ms	(cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
316.0ms	(cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
319.0ms	(cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0)))))
436.0ms	(pow (cbrt (sqrt (sqrt (* 2.0 (+ (- (hypot re im) re) 0))))) 4)

simplify55.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	378	1216
1	1371	1142
2	5001	1123
done	5001	1123

prune407.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.4b

regimes75.0ms

Accuracy

26.5% (4.4b remaining)

Error of 12.1b against oracle of 7.7b and baseline of 13.7b

bsearch65.0ms

Steps

Iters	Range		Point
10	6.203544841310545e+55	2.3069922374741435e+70	1.6666296725523275e+65

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	14
1	33	14
2	33	14
done	33	14

end0.0ms

sample717.0ms

Algorithm

intervals

Results

207.0ms	5947×	body	80	valid
139.0ms	726×	body	2560	valid
79.0ms	528×	body	1280	valid
67.0ms	294×	body	5120	valid
34.0ms	284×	body	640	valid
12.0ms	136×	body	320	valid
5.0ms	85×	body	160	valid