Details

sample69.0ms

Algorithm

intervals

Results

32.0ms	198×	body	80	valid
10.0ms	18×	body	2560	valid
5.0ms	9×	body	5120	valid
5.0ms	12×	body	1280	valid
5.0ms	14×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.3b	(+ (hypot re im) re)

rewrite20.0ms

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:

0.0ms	(hypot re im)
15.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
5.0ms	(+ (hypot re im) re)

series378.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(hypot re im)
250.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
73.0ms	(+ (hypot re im) re)

simplify1.9s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	3803
2	628
1	190
0	89

prune352.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.3b	(+ (hypot re im) re)
0.3b	(+ (hypot re im) re)
0.4b	(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))

rewrite50.0ms

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` `insert-posit16` `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 → 112

Calls

4 calls:

0.0ms	(hypot re im)
5.0ms	(+ (hypot re im) re)
9.0ms	(+ (hypot re im) re)
34.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(hypot re im)
59.0ms	(+ (hypot re im) re)
87.0ms	(+ (hypot re im) re)
82.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt (+ (hypot re im) re)))

simplify1.8s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	780
1	212
0	106

prune643.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (hypot re im) re)) (cbrt (+ (hypot re im) re)))
0.5b	(cbrt (+ (hypot re im) re))
0.5b	(cbrt (+ (hypot re im) re))
0.5b	(cbrt (+ (hypot re im) re))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
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 → 107

Calls

4 calls:

33.0ms	(* (cbrt (+ (hypot re im) re)) (cbrt (+ (hypot re im) re)))
3.0ms	(cbrt (+ (hypot re im) re))
3.0ms	(cbrt (+ (hypot re im) re))
7.0ms	(cbrt (+ (hypot re im) re))

series870.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* (cbrt (+ (hypot re im) re)) (cbrt (+ (hypot re im) re)))
202.0ms	(cbrt (+ (hypot re im) re))
197.0ms	(cbrt (+ (hypot re im) re))
253.0ms	(cbrt (+ (hypot re im) re))

simplify1.4s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	1178
1	324
0	142

prune848.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.0b	(hypot re im)
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
7.9b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`*-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×	`pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 89

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
18.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
18.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series313.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(hypot re im)
53.0ms	(hypot re im)
84.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
102.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	711
1	197
0	90

prune500.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.0b

regimes175.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

855.0ms	6065×	body	80	valid
563.0ms	648×	body	2560	valid
525.0ms	284×	body	640	valid
289.0ms	471×	body	1280	valid
279.0ms	294×	body	5120	valid
53.0ms	164×	body	320	valid
17.0ms	74×	body	160	valid