Details

sample47.0ms

Algorithm

intervals

Results

11.0ms	197×	body	80	valid
9.0ms	24×	body	2560	valid
6.0ms	22×	body	1280	valid
3.0ms	8×	body	5120	valid
1.0ms	3×	body	640	valid
0.0ms	2×	body	320	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	32
3	32
2	30
1	24
0	12

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

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` `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 → 42

Calls

3 calls:

0.0ms	(hypot re im)
29.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
6.0ms	(+ (hypot re im) re)

series426.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(hypot re im)
266.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
106.0ms	(+ (hypot re im) re)

simplify1.7s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
3	3673
2	612
1	187
0	86

prune356.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(+ re (hypot re im))
0.0b	(+ re (hypot re im))
0.4b	(* (sqrt (+ re (hypot re im))) (sqrt (+ re (hypot re im))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `sqrt-prod`
19×	`pow1`
14×	`add-cube-cbrt`
12×	`sqrt-div`
11×	`swap-sqr`
8×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out` `add-log-exp`
7×	`associate-r` `associate-l`
6×	`fma-def` `add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`+-commutative` `sum-log` `associate-l/` `associate-r/`
1×	`pow2` `hypot-udef` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 108

Calls

4 calls:

0.0ms	(hypot re im)
5.0ms	(+ re (hypot re im))
8.0ms	(+ re (hypot re im))
42.0ms	(* (sqrt (+ re (hypot re im))) (sqrt (+ re (hypot re im))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(hypot re im)
90.0ms	(+ re (hypot re im))
77.0ms	(+ re (hypot re im))
95.0ms	(* (sqrt (+ re (hypot re im))) (sqrt (+ re (hypot re im))))

simplify1.2s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	780
1	210
0	103

prune670.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.2b

localize26.0ms

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	(sqrt (hypot re im))
0.0b	(sqrt (hypot re im))
14.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
8×	`add-sqr-sqrt`
7×	`sqrt-prod`
6×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rem-sqrt-square`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 53

Calls

4 calls:

4.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series773.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
123.0ms	(sqrt (hypot re im))
120.0ms	(sqrt (hypot re im))
209.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify2.4s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
3	4339
2	709
1	195
0	90

prune358.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.2b

localize19.0ms

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)) (cbrt (hypot re im)))
10.0b	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `+-commutative` `sum-log` `fma-def` `flip3-+` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 82

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
23.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
23.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

series621.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (hypot re im))
185.0ms	(cbrt (hypot re im))
179.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
89.0ms	(+ (* (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im))) re)

simplify1.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1081
1	252
0	105

prune481.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.2b

regimes187.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

934.0ms	6072×	body	80	valid
301.0ms	647×	body	2560	valid
187.0ms	467×	body	1280	valid
184.0ms	285×	body	5120	valid
82.0ms	78×	body	160	valid
82.0ms	296×	body	640	valid
30.0ms	155×	body	320	valid