Details

sample26.0ms

Algorithm

intervals

Results

6.0ms	191×	body	80	valid
4.0ms	24×	body	2560	valid
2.0ms	15×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	6×	body	5120	valid
0.0ms	3×	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: 41.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (sqrt (+ (* re re) (* im im))) re)
31.7b	(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

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:

32.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
8.0ms	(sqrt (+ (* re re) (* im im)))

series85.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ (sqrt (+ (* re re) (* im im))) re)
39.0ms	(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Counts

44 → 44

Iterations

Useful iterations: 4 (85.0ms)

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

prune135.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(hypot re im)
0.5b	(+ (* (sqrt 1) (hypot re im)) re)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

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

series105.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(hypot re im)
57.0ms	(+ (* (sqrt 1) (hypot re im)) re)

simplify97.0ms

Counts

30 → 30

Iterations

Useful iterations: 4 (94.0ms)

Iter	Nodes	Cost
0	111	124
1	285	109
2	788	106
3	3168	104
4	5001	103
done	5001	103

prune105.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.7b

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 (hypot re im)))
7.3b	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

0.0ms	(hypot re im)
0.0ms	(hypot re im)
15.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
30.0ms	(+ (* (sqrt 1) (* (sqrt (hypot re im)) (sqrt (hypot re im)))) re)

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

simplify177.0ms

Counts

97 → 97

Iterations

Useful iterations: 3 (172.0ms)

Iter	Nodes	Cost
0	186	390
1	680	325
2	4049	286
3	5001	282
done	5001	282

prune248.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.7b

localize22.0ms

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))
8.0b	(+ (* (sqrt 1) (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im))))) re)

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`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×	`pow1/3`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
138.0ms	(+ (* (sqrt 1) (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im))))) re)

series392.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (hypot re im))
110.0ms	(cbrt (hypot re im))
109.0ms	(cbrt (hypot re im))
60.0ms	(+ (* (sqrt 1) (* (sqrt (* (cbrt (hypot re im)) (cbrt (hypot re im)))) (* (sqrt (cbrt (hypot re im))) (sqrt (hypot re im))))) re)

simplify124.0ms

Counts

65 → 65

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	160	523
1	535	462
2	3004	435
3	5001	426
done	5001	426

prune300.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.7b

regimes171.0ms

Accuracy

19.5% (4.7b remaining)

Error of 12.1b against oracle of 7.4b and baseline of 13.2b

bsearch37.0ms

Steps

Iters	Range		Point
6	-2.781626725963439e+169	-2.703227677368954e+168	-9.189817498010996e+168

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14
done	30	14

end0.0ms

sample692.0ms

Algorithm

intervals

Results

197.0ms	6052×	body	80	valid
139.0ms	720×	body	2560	valid
67.0ms	445×	body	1280	valid
65.0ms	273×	body	5120	valid
36.0ms	297×	body	640	valid
15.0ms	145×	body	320	valid
4.0ms	68×	body	160	valid