Details

sample103.0ms

Algorithm

intervals

Results

26.0ms	188×	body	80	valid
14.0ms	16×	body	2560	valid
13.0ms	17×	body	1280	valid
10.0ms	11×	body	5120	valid
8.0ms	14×	body	640	valid
3.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.0b	(hypot re im)
1.1b	(+ (hypot re im) re)

rewrite18.0ms

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:

8.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
0.0ms	(hypot re im)
9.0ms	(+ (hypot re im) re)

series434.0ms

Counts

3 → 9

Calls

3 calls:

254.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
79.0ms	(hypot re im)
100.0ms	(+ (hypot re im) re)

simplify2.8s

Counts

54 → 54

Iterations

Iter	Nodes
4	4081
3	1315
2	474
1	189
0	89

prune549.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.1b

localize36.0ms

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))
9.9b	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`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`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 57

Calls

4 calls:

2.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
26.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series524.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(cbrt (hypot re im))
150.0ms	(cbrt (hypot re im))
141.0ms	(cbrt (hypot re im))
80.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify2.1s

Counts

69 → 69

Iterations

Iter	Nodes
4	3712
3	1168
2	408
1	152
0	65

prune781.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 14.0b

localize45.0ms

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))
11.6b	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) re)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`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`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 57

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
65.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) re)

series610.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (hypot re im))
192.0ms	(cbrt (hypot re im))
150.0ms	(cbrt (hypot re im))
107.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (* (sqrt (cbrt (hypot re im))) (sqrt (cbrt (hypot re im))))) re)

simplify5.1s

Counts

69 → 69

Iterations

Iter	Nodes
4	7199
3	1747
2	524
1	164
0	67

prune990.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 14.0b

localize18.0ms

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)
16.3b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite9.0ms

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)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series673.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
76.0ms	(hypot re im)
60.0ms	(hypot re im)
211.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.8s

Counts

59 → 59

Iterations

Iter	Nodes
4	3022
3	1016
2	364
1	150
0	77

prune686.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 14.0b

regimes212.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	694×	body	2560	valid
751.0ms	5994×	body	80	valid
348.0ms	517×	body	1280	valid
337.0ms	290×	body	5120	valid
154.0ms	286×	body	640	valid
79.0ms	147×	body	320	valid
16.0ms	72×	body	160	valid