Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	199×	body	80	valid
4.0ms	20×	body	2560	valid
2.0ms	16×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	30	8
2	33	8
3	33	8
done	33	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.9b	(+ (sqrt (+ (* re re) (* im im))) re)
28.4b	(sqrt (+ (* re re) (* im im)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

35.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series87.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms	(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Counts

44 → 44

Iterations

Useful iterations: 4 (87.0ms)

Iter	Nodes	Cost
0	155	205
1	421	183
2	1067	180
3	3190	179
4	5001	178
done	5001	178

prune124.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.9b	(+ re (hypot re im))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 27

Calls

2 calls:

0.0ms	(hypot re im)
5.0ms	(+ re (hypot re im))

series108.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(hypot re im)
61.0ms	(+ re (hypot re im))

simplify77.0ms

Counts

33 → 33

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	88	84
1	176	78
2	370	78
3	1004	78
4	3138	78
5	5001	78
done	5001	78

prune99.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 7.2b

localize11.0ms

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)))
7.4b	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

rewrite24.0ms

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)
16.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
6.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(hypot re im)
46.0ms	(hypot re im)
52.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
57.0ms	(+ re (* (sqrt (hypot re im)) (sqrt (hypot re im))))

simplify180.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	171	341
1	603	286
2	3648	275
3	5001	275
done	5001	275

prune247.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
0.6b	(cbrt (hypot re im))
7.4b	(+ re (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))))

rewrite10.0ms

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))
7.0ms	(+ re (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (hypot re im))
113.0ms	(cbrt (hypot re im))
119.0ms	(cbrt (hypot re im))
57.0ms	(+ re (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im)))))

simplify83.0ms

Counts

67 → 67

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	153	482
1	514	416
2	2454	402
3	5001	378
done	5001	378

prune287.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.2b

regimes98.0ms

Accuracy

26.4% (5.2b remaining)

Error of 12.5b against oracle of 7.3b and baseline of 14.4b

bsearch147.0ms

Steps

Iters	Range	Point
7	-1.833925802296283e-14	-6.965098439168222e-16	-1.1425655951183048e-14
9	-2.9757909971743123e+131	-3.709175225212192e+126	-9.345587729548568e+128
7	-1.820113320418141e+229	-1.1214053550881e+228	-1.1333132744990301e+228

Iters

Range

Point

-1.833925802296283e-14

-6.965098439168222e-16

-1.1425655951183048e-14

-2.9757909971743123e+131

-3.709175225212192e+126

-9.345587729548568e+128

-1.820113320418141e+229

-1.1214053550881e+228

-1.1333132744990301e+228

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	40	34
1	45	17
2	48	17
3	48	17
done	48	17

end0.0ms

sample698.0ms

Algorithm

intervals

Results

192.0ms	6026×	body	80	valid
136.0ms	688×	body	2560	valid
80.0ms	499×	body	1280	valid
63.0ms	281×	body	5120	valid
34.0ms	294×	body	640	valid
13.0ms	139×	body	320	valid
4.0ms	73×	body	160	valid