Details

sample81.0ms

Algorithm

intervals

Results

30.0ms	198×	body	80	valid
14.0ms	28×	body	2560	valid
5.0ms	9×	body	5120	valid
4.0ms	9×	body	1280	valid
2.0ms	6×	body	640	valid
1.0ms	6×	body	320	valid

simplify25.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize22.0ms

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))

rewrite12.0ms

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)
4.0ms	(+ (hypot re im) re)
7.0ms	(sqrt (* (+ (hypot re im) re) 2.0))

series431.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(hypot re im)
87.0ms	(+ (hypot re im) re)
283.0ms	(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

prune333.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.3b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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:

11.0ms	(sqrt (+ (hypot re im) re))
0.0ms	(hypot re im)
7.0ms	(+ (hypot re im) re)
21.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

series612.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(sqrt (+ (hypot re im) re))
62.0ms	(hypot re im)
70.0ms	(+ (hypot re im) re)
257.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1285
1	307
0	135

prune564.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

0.0ms	(hypot re im)
4.0ms	(+ (hypot re im) re)
39.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
93.0ms	(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series752.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(hypot re im)
89.0ms	(+ (hypot re im) re)
361.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
240.0ms	(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.7s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
2	2175
1	397
0	157

prune719.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 11.2b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.2b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0)))
0.3b	(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
14.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-prod`
24×	`add-sqr-sqrt`
18×	`associate-r`
16×	`pow1`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow-prod-down`
7×	`associate-l`
6×	`unswap-sqr`
5×	`sqrt-pow1` `pow1/2`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`
1×	`hypot-udef` `fma-udef`

Counts

4 → 86

Calls

4 calls:

0.0ms	(hypot re im)
14.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0)))
47.0ms	(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series1.1s

Counts

4 → 12

Calls

4 calls:

75.0ms	(hypot re im)
473.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0)))
332.0ms	(* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
204.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1975
1	381
0	154

prune522.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.2b

regimes183.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

485.0ms	253×	body	640	valid
416.0ms	6072×	body	80	valid
352.0ms	694×	body	2560	valid
234.0ms	491×	body	1280	valid
177.0ms	286×	body	5120	valid
25.0ms	136×	body	320	valid
8.0ms	68×	body	160	valid