Details

sample80.0ms

Algorithm

intervals

Results

21.0ms	21×	body	2560	valid
18.0ms	203×	body	80	valid
4.0ms	11×	body	1280	valid
3.0ms	5×	body	5120	valid
3.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	31
3	31
2	29
1	24
0	12

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize58.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.3b	(sqrt (* (+ (hypot re im) re) 2.0))
0.8b	(+ (hypot re im) re)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `hypot-udef` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

3 → 45

Calls

3 calls:

1.0ms	(hypot re im)
22.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
16.0ms	(+ (hypot re im) re)

series569.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(hypot re im)
376.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
107.0ms	(+ (hypot re im) re)

simplify3.8s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	1405
2	487
1	190
0	89

prune847.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.6b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (+ (hypot re im) re))
0.4b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
0.8b	(+ (hypot re im) re)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`sqrt-prod`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`associate-l`
6×	`add-cbrt-cube` `associate-r` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out`
2×	`associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `hypot-udef` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 85

Calls

4 calls:

1.0ms	(hypot re im)
11.0ms	(sqrt (+ (hypot re im) re))
43.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
12.0ms	(+ (hypot re im) re)

series773.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(hypot re im)
216.0ms	(sqrt (+ (hypot re im) re))
351.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
109.0ms	(+ (hypot re im) re)

simplify6.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	2516
2	826
1	311
0	139

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.6b

localize83.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.3b	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
6.3b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`pow1`
22×	`sqrt-prod`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`sqrt-pow1`
10×	`pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-sqr`
2×	`flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`pow2` `+-commutative` `rem-sqrt-square` `sum-log` `rem-square-sqrt` `fma-def` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 99

Calls

4 calls:

5.0ms	(sqrt (hypot re im))
34.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
22.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
15.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series700.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(sqrt (hypot re im))
350.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
95.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
116.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify5.3s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
3	2590
2	839
1	340
0	147

prune1.2s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 11.5b

localize181.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
6.8b	(+ (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))) re)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 57

Calls

4 calls:

3.0ms	(cbrt (hypot re im))
3.0ms	(cbrt (hypot re im))
3.0ms	(cbrt (hypot re im))
101.0ms	(+ (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))) re)

series855.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt (hypot re im))
252.0ms	(cbrt (hypot re im))
236.0ms	(cbrt (hypot re im))
116.0ms	(+ (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))) re)

simplify5.2s

Counts

69 → 69

Iterations

Iter	Nodes
done	5035
3	1787
2	509
1	162
0	68

prune1.0s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 11.5b

regimes799.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

566.0ms	5997×	body	80	valid
532.0ms	480×	body	1280	valid
359.0ms	717×	body	2560	valid
176.0ms	295×	body	5120	valid
77.0ms	301×	body	640	valid
24.0ms	136×	body	320	valid
13.0ms	74×	body	160	valid