Details

sample67.0ms

Algorithm

intervals

Results

17.0ms	196×	body	80	valid
12.0ms	23×	body	2560	valid
7.0ms	17×	body	1280	valid
4.0ms	7×	body	5120	valid
2.0ms	5×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize58.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
0.0b	(hypot re im)
1.3b	(+ re (hypot re im))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

16.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
1.0ms	(hypot re im)
12.0ms	(+ re (hypot re im))

series691.0ms

Counts

3 → 9

Calls

3 calls:

455.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
106.0ms	(hypot re im)
129.0ms	(+ re (hypot re im))

simplify6.1s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
4	4821
3	1399
2	477
1	187
0	86

prune509.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ re (hypot re im)))
0.0b	(hypot re im)
0.4b	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
1.3b	(+ re (hypot re im))

rewrite95.0ms

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-exp-log` `associate-r` `add-cbrt-cube` `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` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 81

Calls

4 calls:

14.0ms	(sqrt (+ re (hypot re im)))
2.0ms	(hypot re im)
63.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
12.0ms	(+ re (hypot re im))

series805.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(sqrt (+ re (hypot re im)))
90.0ms	(hypot re im)
353.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
126.0ms	(+ re (hypot re im))

simplify4.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	5007
3	2486
2	821
1	306
0	135

prune764.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.4b

localize121.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (sqrt (+ re (hypot re im))) (sqrt 2.0)))
1.3b	(+ re (hypot re im))
1.3b	(+ re (hypot re im))
1.3b	(+ re (hypot re im))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

30.0ms	(cbrt (* (sqrt (+ re (hypot re im))) (sqrt 2.0)))
13.0ms	(+ re (hypot re im))
13.0ms	(+ re (hypot re im))
13.0ms	(+ re (hypot re im))

series929.0ms

Counts

4 → 12

Calls

4 calls:

584.0ms	(cbrt (* (sqrt (+ re (hypot re im))) (sqrt 2.0)))
102.0ms	(+ re (hypot re im))
127.0ms	(+ re (hypot re im))
114.0ms	(+ re (hypot re im))

simplify3.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5005
3	1973
2	583
1	215
0	100

prune995.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.1b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

0.0ms	(hypot re im)
16.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
21.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
11.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series732.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(hypot re im)
436.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
93.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
101.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify4.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
3	2306
2	716
1	283
0	129

prune779.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.4b

regimes345.0ms

Accuracy

0% (0.6b remaining)

Error of 13.5b against oracle of 13.0b and baseline of 13.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	300×	body	5120	valid
736.0ms	6026×	body	80	valid
405.0ms	695×	body	2560	valid
303.0ms	485×	body	1280	valid
85.0ms	265×	body	640	valid
44.0ms	152×	body	320	valid
12.0ms	77×	body	160	valid