Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
3.0ms	18×	body	2560	valid
3.0ms	17×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	6×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite7.0ms

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:

4.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
0.0ms	(hypot re im)
3.0ms	(+ re (hypot re im))

series291.0ms

Counts

3 → 9

Calls

3 calls:

187.0ms	(sqrt (* (+ re (hypot re im)) 2.0))
48.0ms	(hypot re im)
55.0ms	(+ re (hypot re im))

simplify674.0ms

Counts

51 → 51

Iterations

Useful iterations: done (673.0ms)

Iter	Nodes	Cost
0	86	414
1	187	377
2	491	354
3	1479	345
done	5000	344

prune148.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.2b

localize10.0ms

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)))
6.7b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `pow-sqr`
2×	`hypot-udef`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 87

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
9.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
2.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series198.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot re im)
45.0ms	(hypot re im)
49.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
56.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify2.8s

Counts

99 → 99

Iterations

Useful iterations: 3 (424.0ms)

Iter	Nodes	Cost
0	87	990
1	170	535
2	530	501
3	2956	485
done	5000	485

prune243.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.2b

localize12.0ms

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 (* 1 (hypot re im))))
6.7b	(+ re (* (sqrt (hypot re im)) (sqrt (* 1 (hypot re im)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`pow1`
9×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`sqrt-prod`
6×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-r` `log1p-expm1-u`
3×	`fma-def`
2×	`hypot-udef` `pow1/2` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sqrt-unprod` `swap-sqr` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 66

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
9.0ms	(* (sqrt (hypot re im)) (sqrt (* 1 (hypot re im))))
2.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (* 1 (hypot re im)))))

series200.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot re im)
45.0ms	(hypot re im)
48.0ms	(* (sqrt (hypot re im)) (sqrt (* 1 (hypot re im))))
58.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (* 1 (hypot re im)))))

simplify3.6s

Counts

78 → 78

Iterations

Useful iterations: 3 (246.0ms)

Iter	Nodes	Cost
0	80	833
1	166	442
2	473	402
3	1179	388
4	3766	388
done	5001	388

prune259.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
8.2b	(+ re (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

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

series422.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (sqrt (hypot re im)) (fabs (cbrt (hypot re im))))
108.0ms	(cbrt (hypot re im))
111.0ms	(cbrt (hypot re im))
104.0ms	(+ re (* (* (sqrt (hypot re im)) (fabs (cbrt (hypot re im)))) (sqrt (cbrt (hypot re im)))))

simplify2.4s

Counts

78 → 78

Iterations

Useful iterations: 3 (460.0ms)

Iter	Nodes	Cost
0	129	1122
1	320	1052
2	1122	929
3	4961	906
done	5000	906

prune294.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 13.2b

regimes132.0ms

Accuracy

0% (0.3b remaining)

Error of 13.5b against oracle of 13.2b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	12	10
done	12	10

end0.0ms

sample672.0ms

Algorithm

intervals

Results

197.0ms	6020×	body	80	valid
139.0ms	719×	body	2560	valid
75.0ms	479×	body	1280	valid
66.0ms	266×	body	5120	valid
39.0ms	280×	body	640	valid
15.0ms	163×	body	320	valid
4.0ms	73×	body	160	valid