Details

sample62.0ms

Algorithm

intervals

Results

14.0ms	185×	body	80	valid
14.0ms	29×	body	2560	valid
8.0ms	13×	body	5120	valid
5.0ms	14×	body	1280	valid
3.0ms	10×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	30	10
3	32	10
done	32	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ re (hypot re im)) 2.0))
0.6b	(+ re (hypot re im))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`add-exp-log` `expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `hypot-udef` `pow1/2` `pow-prod-down` `sum-log` `sqrt-prod` `distribute-lft-out`

Counts

3 → 42

Calls

3 calls:

0.0ms	(hypot re im)
25.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
6.0ms	(+ re (hypot re im))

series449.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(hypot re im)
284.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
79.0ms	(+ re (hypot re im))

simplify2.3s

Counts

51 → 51

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	86	414
1	187	377
2	617	354
3	3785	345
done	5000	344

prune197.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ re (hypot re im)))
0.0b	(hypot re im)
0.3b	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
0.6b	(+ re (hypot re im))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`sqrt-prod`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`associate-l`
6×	`add-exp-log` `associate-r` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out`
2×	`associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `hypot-udef` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 81

Calls

4 calls:

15.0ms	(sqrt (+ re (hypot re im)))
1.0ms	(hypot re im)
36.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
6.0ms	(+ re (hypot re im))

series606.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(sqrt (+ re (hypot re im)))
67.0ms	(hypot re im)
245.0ms	(* (sqrt (+ re (hypot re im))) (sqrt 2.0))
81.0ms	(+ re (hypot re im))

simplify954.0ms

Counts

93 → 93

Iterations

Useful iterations: done (952.0ms)

Iter	Nodes	Cost
0	135	898
1	306	827
2	1268	780
done	5000	771

prune394.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (hypot re im))
0.0b	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
9.6b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
7.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
26.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
12.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series560.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (hypot re im))
293.0ms	(sqrt (* (+ re (* (sqrt (hypot re im)) (sqrt (hypot re im)))) 2.0))
77.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
78.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify1.7s

Counts

109 → 109

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	143	1359
1	337	767
2	1439	698
done	5001	689

prune356.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 13.7b

localize48.0ms

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))
7.9b	(+ re (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `pow1/3`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
14.0ms	(+ re (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))))

series546.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (hypot re im))
154.0ms	(cbrt (hypot re im))
144.0ms	(cbrt (hypot re im))
79.0ms	(+ re (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))))

simplify3.0s

Counts

67 → 67

Iterations

Useful iterations: 3 (924.0ms)

Iter	Nodes	Cost
0	66	842
1	156	714
2	613	638
3	4163	595
done	5000	595

prune460.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.7b

regimes146.0ms

Accuracy

0% (0.6b remaining)

Error of 13.7b against oracle of 13.1b and baseline of 13.7b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	11
1	13	11
done	13	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

622.0ms	306×	body	5120	valid
590.0ms	6000×	body	80	valid
309.0ms	694×	body	2560	valid
238.0ms	523×	body	1280	valid
67.0ms	254×	body	640	valid
27.0ms	144×	body	320	valid
10.0ms	79×	body	160	valid