Details

sample199.0ms

Algorithm

intervals

Results

28.0ms	197×	body	80	valid
20.0ms	24×	body	1280	valid
13.0ms	15×	body	2560	valid
12.0ms	8×	body	5120	valid
5.0ms	8×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify97.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.2b	(- (hypot re im) re)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

0.0ms	(hypot re im)
12.0ms	(- (hypot re im) re)

series157.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(hypot re im)
95.0ms	(- (hypot re im) re)

simplify919.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	2000
4	1591
3	665
2	263
1	142
0	71

prune234.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
0.4b	(cbrt (- (hypot re im) re))
0.4b	(cbrt (- (hypot re im) re))
0.4b	(cbrt (- (hypot re im) re))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 113

Calls

4 calls:

31.0ms	(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
6.0ms	(cbrt (- (hypot re im) re))
6.0ms	(cbrt (- (hypot re im) re))
6.0ms	(cbrt (- (hypot re im) re))

series864.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(* (cbrt (- (hypot re im) re)) (cbrt (- (hypot re im) re)))
230.0ms	(cbrt (- (hypot re im) re))
201.0ms	(cbrt (- (hypot re im) re))
172.0ms	(cbrt (- (hypot re im) re))

simplify673.0ms

Counts

125 → 125

Iterations

Iter	Nodes
done	2000
2	851
1	329
0	151

prune628.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (- (hypot re im) re))
0.4b	(cbrt (- (hypot re im) re))
0.4b	(cbrt (- (hypot re im) re))
0.4b	(* (sqrt (cbrt (- (hypot re im) re))) (sqrt (cbrt (- (hypot re im) re))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
50×	`sqrt-prod`
45×	`cbrt-prod`
39×	`*-un-lft-identity`
19×	`pow1` `add-cube-cbrt`
18×	`cbrt-div`
15×	`swap-sqr`
14×	`sqrt-pow1`
12×	`sqrt-div`
11×	`associate-r` `associate-l`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `unswap-sqr`
8×	`pow1/2`
7×	`difference-of-squares`
6×	`add-cbrt-cube` `add-exp-log` `pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `pow-sqr` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-l/` `associate-r/`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 139

Calls

4 calls:

3.0ms	(cbrt (- (hypot re im) re))
3.0ms	(cbrt (- (hypot re im) re))
5.0ms	(cbrt (- (hypot re im) re))
48.0ms	(* (sqrt (cbrt (- (hypot re im) re))) (sqrt (cbrt (- (hypot re im) re))))

series785.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt (- (hypot re im) re))
197.0ms	(cbrt (- (hypot re im) re))
185.0ms	(cbrt (- (hypot re im) re))
201.0ms	(* (sqrt (cbrt (- (hypot re im) re))) (sqrt (cbrt (- (hypot re im) re))))

simplify939.0ms

Counts

151 → 151

Iterations

Iter	Nodes
done	2000
3	1767
2	714
1	315
0	159

prune843.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
6.3b	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
15×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`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×	`rem-sqrt-square`
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 → 104

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
12.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series406.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(sqrt (hypot re im))
136.0ms	(sqrt (hypot re im))
73.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
84.0ms	(- (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify997.0ms

Counts

116 → 116

Iterations

Iter	Nodes
done	2000
3	1869
2	672
1	285
0	127

prune393.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.7b

regimes501.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	9

end0.0ms

sample2.6s

Algorithm

intervals

Results

874.0ms	6067×	body	80	valid
628.0ms	648×	body	2560	valid
340.0ms	484×	body	1280	valid
275.0ms	325×	body	5120	valid
183.0ms	263×	body	640	valid
76.0ms	144×	body	320	valid
15.0ms	69×	body	160	valid