Details

sample37.0ms

Algorithm

intervals

Results

9.0ms	198×	body	80	valid
8.0ms	28×	body	2560	valid
3.0ms	9×	body	5120	valid
2.0ms	9×	body	1280	valid
1.0ms	6×	body	640	valid
1.0ms	6×	body	320	valid

simplify11.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
3	32
2	30
1	24
0	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(+ (hypot re im) re)
0.2b	(sqrt (* (+ (hypot re im) re) 2.0))

rewrite44.0ms

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` `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 → 42

Calls

3 calls:

0.0ms	(hypot re im)
10.0ms	(+ (hypot re im) re)
32.0ms	(sqrt (* (+ (hypot re im) re) 2.0))

series377.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(hypot re im)
73.0ms	(+ (hypot re im) re)
235.0ms	(sqrt (* (+ (hypot re im) re) 2.0))

simplify1.9s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
3	3812
2	623
1	187
0	86

prune401.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

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` `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 → 81

Calls

4 calls:

12.0ms	(sqrt (+ re (hypot re im)))
0.0ms	(hypot re im)
8.0ms	(+ re (hypot re im))
38.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))

series641.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(sqrt (+ re (hypot re im)))
65.0ms	(hypot re im)
87.0ms	(+ re (hypot re im))
296.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))

simplify852.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1276
1	307
0	135

prune559.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(+ (hypot re im) re)
0.2b	(* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re)))
0.2b	(* (* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

31×	`sqrt-prod`
25×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`pow1` `associate-r`
13×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-l` `pow-prod-down`
6×	`add-log-exp` `unswap-sqr`
5×	`sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `sqrt-div` `prod-exp` `associate-*r/` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `sqrt-unprod` `flip-+`
2×	`associate-l/` `-commutative` `distribute-lft-out`
1×	`+-commutative` `hypot-udef` `sum-log`

Counts

4 → 98

Calls

4 calls:

0.0ms	(hypot re im)
7.0ms	(+ (hypot re im) re)
23.0ms	(* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re)))
70.0ms	(* (* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0)))

series804.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(hypot re im)
97.0ms	(+ (hypot re im) re)
349.0ms	(* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re)))
295.0ms	(* (* (sqrt (sqrt 2.0)) (sqrt (+ (hypot re im) re))) (sqrt (sqrt 2.0)))

simplify1.3s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	2102
1	409
0	161

prune671.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt re)
0.5b	(cbrt re)
0.5b	(* (cbrt re) (cbrt re))
13.8b	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt re)
1.0ms	(cbrt re)
16.0ms	(* (cbrt re) (cbrt re))
1.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

series1.2s

Counts

4 → 12

Calls

4 calls:

292.0ms	(cbrt re)
301.0ms	(cbrt re)
337.0ms	(* (cbrt re) (cbrt re))
302.0ms	(fma (* (cbrt re) (cbrt re)) (cbrt re) (hypot re im))

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	769
1	160
0	80

prune624.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 11.2b

regimes168.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample1.9s

Algorithm

intervals

Results

776.0ms	6072×	body	80	valid
300.0ms	491×	body	1280	valid
274.0ms	694×	body	2560	valid
157.0ms	253×	body	640	valid
120.0ms	286×	body	5120	valid
23.0ms	136×	body	320	valid
8.0ms	68×	body	160	valid