Details

sample51.0ms

Algorithm

intervals

Results

13.0ms	193×	body	80	valid
9.0ms	23×	body	2560	valid
5.0ms	16×	body	1280	valid
3.0ms	8×	body	5120	valid
1.0ms	6×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.8b	(+ (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` `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)
10.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms	(+ (hypot re im) re)

series408.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(hypot re im)
260.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
83.0ms	(+ (hypot re im) re)

simplify1.7s

Counts

51 → 51

Iterations

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

prune357.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.4b

localize21.0ms

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)))
6.2b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-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` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `fma-def` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 95

Calls

4 calls:

1.0ms	(sqrt (hypot re im))
1.0ms	(sqrt (hypot re im))
11.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
14.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series415.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (hypot re im))
118.0ms	(sqrt (hypot re im))
67.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
101.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify843.0ms

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	1062
1	251
0	103

prune580.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 13.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (hypot re im)))
0.5b	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
0.5b	(* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)))
10.3b	(+ (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im))) re)

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-pow1`
81×	`sqrt-prod`
73×	`pow1`
56×	`add-sqr-sqrt`
51×	`pow1/2`
43×	`pow-prod-up`
20×	`*-un-lft-identity` `add-cube-cbrt`
17×	`swap-sqr`
15×	`associate-r`
13×	`pow-sqr`
12×	`pow-prod-down`
11×	`add-cbrt-cube` `add-exp-log` `unswap-sqr`
10×	`associate-l`
7×	`pow-plus`
6×	`add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sqrt-unprod`
2×	`rem-sqrt-square` `*-commutative`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `fma-def` `flip3-+` `flip-+`

Counts

4 → 166

Calls

4 calls:

2.0ms	(sqrt (sqrt (hypot re im)))
24.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
56.0ms	(* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)))
69.0ms	(+ (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im))) re)

series424.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(sqrt (sqrt (hypot re im)))
143.0ms	(* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im))))
60.0ms	(* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im)))
75.0ms	(+ (* (* (sqrt (sqrt (hypot re im))) (sqrt (sqrt (hypot re im)))) (sqrt (hypot re im))) re)

simplify3.8s

Counts

178 → 178

Iterations

Iter	Nodes
done	5001
2	2895
1	463
0	180

prune666.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 13.4b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (sqrt (sqrt (hypot re im)))) 3))
0.5b	(* (* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (sqrt (sqrt (hypot re im)))) 3)) (sqrt (hypot re im)))
0.7b	(pow (sqrt (sqrt (sqrt (hypot re im)))) 3)
12.5b	(+ (* (* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (sqrt (sqrt (hypot re im)))) 3)) (sqrt (hypot re im))) re)

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

201×	`sqrt-prod`
104×	`add-sqr-sqrt`
40×	`unpow-prod-down` `cube-prod` `unswap-sqr`
36×	`associate-r`
28×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-exp-log`
13×	`associate-l`
12×	`add-cbrt-cube`
11×	`pow1`
10×	`prod-exp`
9×	`sqrt-pow1`
7×	`pow-pow`
6×	`add-log-exp` `sqr-pow`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`pow-to-exp` `pow-unpow` `pow1/2` `pow-exp`
2×	`cube-mult` `unpow3` `*-commutative`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `pow-prod-down` `pow-prod-up` `flip-+` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 185

Calls

4 calls:

37.0ms	(* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (sqrt (sqrt (hypot re im)))) 3))
54.0ms	(* (* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (sqrt (sqrt (hypot re im)))) 3)) (sqrt (hypot re im)))
7.0ms	(pow (sqrt (sqrt (sqrt (hypot re im)))) 3)
52.0ms	(+ (* (* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (sqrt (sqrt (hypot re im)))) 3)) (sqrt (hypot re im))) re)

series524.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (sqrt (sqrt (hypot re im)))) 3))
71.0ms	(* (* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (sqrt (sqrt (hypot re im)))) 3)) (sqrt (hypot re im)))
212.0ms	(pow (sqrt (sqrt (sqrt (hypot re im)))) 3)
101.0ms	(+ (* (* (sqrt (sqrt (sqrt (hypot re im)))) (pow (sqrt (sqrt (sqrt (hypot re im)))) 3)) (sqrt (hypot re im))) re)

simplify3.5s

Counts

197 → 197

Iterations

Iter	Nodes
done	5000
2	3402
1	586
0	201

prune839.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 13.4b

regimes342.0ms

Accuracy

0% (1.5b remaining)

Error of 14.9b against oracle of 13.4b and baseline of 14.9b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

754.0ms	682×	body	2560	valid
451.0ms	5960×	body	80	valid
255.0ms	314×	body	5120	valid
226.0ms	520×	body	1280	valid
172.0ms	282×	body	640	valid
33.0ms	167×	body	320	valid
10.0ms	75×	body	160	valid