Details

sample75.0ms

Algorithm

intervals

Results

21.0ms	188×	body	80	valid
18.0ms	24×	body	2560	valid
9.0ms	11×	body	5120	valid
7.0ms	14×	body	1280	valid
3.0ms	10×	body	320	valid
3.0ms	6×	body	640	valid
1.0ms	3×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	31
3	31
2	29
1	24
0	12

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.2b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

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)
7.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
5.0ms	(+ (hypot re im) re)

series457.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(hypot re im)
310.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
72.0ms	(+ (hypot re im) re)

simplify2.3s

Counts

54 → 54

Iterations

Iter	Nodes
4	4026
3	1321
2	476
1	190
0	89

prune648.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.6b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.2b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 89

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
18.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series313.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(hypot re im)
67.0ms	(hypot re im)
82.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
90.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify2.4s

Counts

101 → 101

Iterations

Iter	Nodes
4	3960
3	1165
2	449
1	188
0	90

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.9b

localize71.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
9.7b	(+ (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-prod` `insert-posit16` `log1p-expm1-u`
3×	`associate-r`
2×	`pow1/3` `unswap-sqr`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 68

Calls

4 calls:

13.0ms	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
22.0ms	(+ (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

series622.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
149.0ms	(cbrt (hypot re im))
177.0ms	(cbrt (hypot re im))
183.0ms	(+ (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))) re)

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
3	3429
2	1016
1	339
0	132

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.8b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (sqrt (hypot re im)))
0.5b	(cbrt (sqrt (hypot re im)))
9.7b	(+ (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) re)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 63

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
2.0ms	(cbrt (sqrt (hypot re im)))
2.0ms	(cbrt (sqrt (hypot re im)))
63.0ms	(+ (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) re)

series635.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (hypot re im))
162.0ms	(cbrt (sqrt (hypot re im)))
145.0ms	(cbrt (sqrt (hypot re im)))
151.0ms	(+ (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (* (cbrt (sqrt (hypot re im))) (cbrt (sqrt (hypot re im)))))) re)

simplify1.6s

Counts

75 → 75

Iterations

Iter	Nodes
3	2741
2	779
1	264
0	113

prune1.2s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 13.8b

regimes342.0ms

Accuracy

0% (0.3b remaining)

Error of 13.7b against oracle of 13.4b and baseline of 13.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample3.0s

Algorithm

intervals

Results

922.0ms	5992×	body	80	valid
896.0ms	733×	body	2560	valid
375.0ms	495×	body	1280	valid
352.0ms	292×	body	5120	valid
160.0ms	271×	body	640	valid
56.0ms	149×	body	320	valid
16.0ms	68×	body	160	valid