Details

sample194.0ms

Algorithm

intervals

Results

35.0ms	204×	body	80	valid
20.0ms	20×	body	2560	valid
8.0ms	7×	body	5120	valid
8.0ms	10×	body	1280	valid
6.0ms	10×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	2×	body	160	valid

simplify117.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	44
5	44
4	42
3	35
2	27
1	19
0	12

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.8b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (- (hypot re im) re) 2.0))
0.0b	(hypot re im)
0.6b	(- (hypot re im) re)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow1`
5×	`add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3--` `sqrt-div` `associate-*l/` `flip--`
1×	`hypot-udef` `sub-neg` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 56

Calls

3 calls:

16.0ms	(sqrt (* (- (hypot re im) re) 2.0))
0.0ms	(hypot re im)
7.0ms	(- (hypot re im) re)

series443.0ms

Counts

3 → 9

Calls

3 calls:

254.0ms	(sqrt (* (- (hypot re im) re) 2.0))
75.0ms	(hypot re im)
113.0ms	(- (hypot re im) re)

simplify2.6s

Counts

65 → 65

Iterations

Iter	Nodes
4	5586
3	1672
2	519
1	232
0	118

prune671.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.6b

localize43.0ms

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)))
6.2b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
13×	`*-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×	`prod-diff` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `sub-neg` `rem-square-sqrt` `pow-plus` `flip3--` `fma-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `difference-of-squares`

Counts

4 → 94

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
16.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
21.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series306.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(hypot re im)
69.0ms	(hypot re im)
57.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
95.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.5s

Counts

106 → 106

Iterations

Iter	Nodes
4	3267
3	1103
2	479
1	211
0	111

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 10.6b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
0.5b	(cbrt (hypot re im))
6.5b	(- (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))) re)

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3` `prod-diff`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
74.0ms	(- (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))) re)

series598.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(cbrt (hypot re im))
146.0ms	(cbrt (hypot re im))
192.0ms	(cbrt (hypot re im))
81.0ms	(- (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))) re)

simplify2.1s

Counts

73 → 73

Iterations

Iter	Nodes
4	3637
3	1302
2	446
1	180
0	87

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 10.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0b	(hypot re im)
0.0b	(hypot re im)
13.0b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

8.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
0.0ms	(hypot re im)
0.0ms	(hypot re im)
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series750.0ms

Counts

4 → 12

Calls

4 calls:

371.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
81.0ms	(hypot re im)
85.0ms	(hypot re im)
212.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.2s

Counts

59 → 59

Iterations

Iter	Nodes
4	4129
3	1236
2	399
1	159
0	81

prune572.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 10.6b

regimes231.0ms

Accuracy

0% (0.3b remaining)

Error of 13.6b against oracle of 13.3b and baseline of 13.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	11
1	11
0	9

end0.0ms

sample3.1s

Algorithm

intervals

Results

980.0ms	735×	body	2560	valid
882.0ms	5985×	body	80	valid
358.0ms	285×	body	5120	valid
357.0ms	472×	body	1280	valid
189.0ms	285×	body	640	valid
63.0ms	170×	body	320	valid
41.0ms	68×	body	160	valid