Details

sample174.0ms

Algorithm

intervals

Results

28.0ms	193×	body	80	valid
17.0ms	24×	body	2560	valid
10.0ms	16×	body	1280	valid
7.0ms	8×	body	5120	valid
3.0ms	7×	body	640	valid
2.0ms	5×	body	320	valid
1.0ms	3×	body	160	valid

simplify83.0ms

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: 14.3b

localize32.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* (- (hypot re im) re) 2.0))
1.1b	(- (hypot re im) re)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

9.0ms	(sqrt (* (- (hypot re im) re) 2.0))
13.0ms	(- (hypot re im) re)

series331.0ms

Counts

2 → 6

Calls

2 calls:

250.0ms	(sqrt (* (- (hypot re im) re) 2.0))
81.0ms	(- (hypot re im) re)

simplify3.4s

Counts

51 → 51

Iterations

Iter	Nodes
4	5135
3	1673
2	511
1	222
0	109

prune449.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.9b

localize21.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
1.1b	(- (hypot re im) re)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`sqrt-prod`
9×	`prod-diff`
8×	`associate-l`
6×	`pow1` `associate-r`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp` `unswap-sqr`
3×	`fma-neg` `pow-prod-down`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `associate-*l/` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `sqrt-unprod` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

2 → 66

Calls

2 calls:

20.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
11.0ms	(- (hypot re im) re)

series383.0ms

Counts

2 → 6

Calls

2 calls:

296.0ms	(* (sqrt (- (hypot re im) re)) (sqrt 2.0))
87.0ms	(- (hypot re im) re)

simplify3.5s

Counts

72 → 72

Iterations

Iter	Nodes
4	4324
3	1721
2	671
1	285
0	135

prune756.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.9b

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.2b	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
1.1b	(- (hypot re im) re)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
32×	`sqrt-prod`
22×	`*-un-lft-identity`
18×	`associate-r` `add-cube-cbrt`
15×	`pow1`
10×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
9×	`associate-l` `prod-diff`
6×	`associate-*l/` `unswap-sqr`
5×	`sqrt-pow1` `pow1/2` `add-log-exp`
4×	`sqrt-div` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `sqrt-unprod` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log`

Counts

3 → 103

Calls

3 calls:

58.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
22.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
5.0ms	(- (hypot re im) re)

series716.0ms

Counts

3 → 9

Calls

3 calls:

281.0ms	(* (* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
358.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (sqrt 2.0)))
76.0ms	(- (hypot re im) re)

simplify1.8s

Counts

112 → 112

Iterations

Iter	Nodes
3	3809
2	1207
1	456
0	188

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.9b

localize68.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
8.9b	(- (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) re)

rewrite58.0ms

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))
44.0ms	(- (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) re)

series565.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (hypot re im))
146.0ms	(cbrt (hypot re im))
170.0ms	(cbrt (hypot re im))
110.0ms	(- (* (cbrt (hypot re im)) (* (cbrt (hypot re im)) (cbrt (hypot re im)))) re)

simplify1.0s

Counts

73 → 73

Iterations

Iter	Nodes
4	2396
3	979
2	379
1	170
0	85

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.9b

regimes161.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	11
1	11
0	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	6052×	body	80	valid
608.0ms	693×	body	2560	valid
340.0ms	485×	body	1280	valid
268.0ms	282×	body	5120	valid
121.0ms	267×	body	640	valid
54.0ms	150×	body	320	valid
16.0ms	71×	body	160	valid