Details

sample79.0ms

Algorithm

intervals

Results

22.0ms	187×	body	80	valid
17.0ms	22×	body	2560	valid
13.0ms	21×	body	1280	valid
6.0ms	11×	body	640	valid
5.0ms	9×	body	5120	valid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.4b

localize36.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* (+ (hypot re im) re) 2.0))
0.7b	(+ (hypot re im) re)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

6.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
5.0ms	(+ (hypot re im) re)

series347.0ms

Counts

2 → 6

Calls

2 calls:

263.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
84.0ms	(+ (hypot re im) re)

simplify1.0s

Counts

40 → 40

Iterations

Iter	Nodes
done	2010
4	2010
3	1359
2	470
1	176
0	77

prune263.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ (hypot re im) re))
0.3b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
0.7b	(+ (hypot re im) re)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

5.0ms	(sqrt (+ (hypot re im) re))
34.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
9.0ms	(+ (hypot re im) re)

series471.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(sqrt (+ (hypot re im) re))
235.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
83.0ms	(+ (hypot re im) re)

simplify985.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	2000
3	2000
2	816
1	297
0	127

prune500.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* (+ (hypot re im) re) 2.0))
0.4b	(* (sqrt (sqrt (* (+ (hypot re im) re) 2.0))) (sqrt (sqrt (* (+ (hypot re im) re) 2.0))))
0.7b	(+ (hypot re im) re)
0.7b	(+ (hypot re im) re)

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

76×	`sqrt-pow1`
64×	`pow1`
27×	`sqrt-prod`
26×	`add-sqr-sqrt` `sqrt-div`
23×	`pow-prod-down`
19×	`pow1/2`
18×	`*-un-lft-identity`
16×	`associate-*l/`
14×	`pow-prod-up` `add-cube-cbrt`
9×	`flip3-+` `swap-sqr` `flip-+`
8×	`pow-sqr` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`fma-def` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`+-commutative` `sum-log` `associate-*r/` `distribute-lft-out`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

13.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
66.0ms	(* (sqrt (sqrt (* (+ (hypot re im) re) 2.0))) (sqrt (sqrt (* (+ (hypot re im) re) 2.0))))
13.0ms	(+ (hypot re im) re)
8.0ms	(+ (hypot re im) re)

series651.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
220.0ms	(* (sqrt (sqrt (* (+ (hypot re im) re) 2.0))) (sqrt (sqrt (* (+ (hypot re im) re) 2.0))))
98.0ms	(+ (hypot re im) re)
78.0ms	(+ (hypot re im) re)

simplify941.0ms

Counts

146 → 146

Iterations

Iter	Nodes
done	2019
3	2019
2	801
1	326
0	152

prune735.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 13.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.2b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
16.9b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 57

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
8.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series823.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(sqrt (hypot re im))
133.0ms	(sqrt (hypot re im))
371.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
178.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.3s

Counts

69 → 69

Iterations

Iter	Nodes
done	2004
4	2004
3	1844
2	531
1	198
0	93

prune334.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 13.9b

regimes228.0ms

Accuracy

0% (0.3b remaining)

Error of 13.4b against oracle of 13.1b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.7s

Algorithm

intervals

Results

866.0ms	5992×	body	80	valid
844.0ms	682×	body	2560	valid
400.0ms	525×	body	1280	valid
267.0ms	306×	body	5120	valid
126.0ms	285×	body	640	valid
41.0ms	132×	body	320	valid
16.0ms	78×	body	160	valid