Details

sample80.0ms

Algorithm

intervals

Results

20.0ms	191×	body	80	valid
14.0ms	14×	body	640	valid
10.0ms	13×	body	5120	valid
10.0ms	18×	body	1280	valid
9.0ms	14×	body	2560	valid
2.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

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:

0.0ms	(hypot re im)
12.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
7.0ms	(+ (hypot re im) re)

series423.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(hypot re im)
279.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
82.0ms	(+ (hypot re im) re)

simplify733.0ms

Counts

54 → 54

Iterations

Iter	Nodes
done	2000
3	1418
2	487
1	190
0	89

prune363.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.1b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

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:

10.0ms	(sqrt (+ (hypot re im) re))
0.0ms	(hypot re im)
33.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
9.0ms	(+ (hypot re im) re)

series621.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(sqrt (+ (hypot re im) re))
75.0ms	(hypot re im)
259.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
101.0ms	(+ (hypot re im) re)

simplify556.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	2008
2	826
1	311
0	139

prune567.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.2b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`pow1`
19×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1`
9×	`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` `hypot-udef` `sum-log` `rem-square-sqrt` `fma-def` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 94

Calls

4 calls:

0.0ms	(hypot re im)
16.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
9.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
9.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series490.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(hypot re im)
244.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
75.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
89.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify479.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	2003
2	695
1	290
0	133

prune498.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.2b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
8.2b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
36×	`sqrt-prod`
34×	`pow1`
20×	`*-un-lft-identity` `add-cube-cbrt`
16×	`sqrt-pow1` `pow1/2` `swap-sqr`
12×	`associate-r` `associate-l`
10×	`pow-prod-up`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp` `unswap-sqr`
6×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 134

Calls

4 calls:

9.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
9.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
9.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
9.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series319.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
67.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
104.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)
72.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.2s

Counts

146 → 146

Iterations

Iter	Nodes
done	2005
3	1118
2	396
1	180
0	82

prune845.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.1b

regimes195.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.3b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	5988×	body	80	valid
599.0ms	695×	body	2560	valid
347.0ms	481×	body	1280	valid
307.0ms	296×	body	5120	valid
143.0ms	302×	body	640	valid
58.0ms	158×	body	320	valid
17.0ms	80×	body	160	valid