Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	185×	body	80	valid
6.0ms	20×	body	1280	valid
5.0ms	21×	body	2560	valid
4.0ms	14×	body	5120	valid
2.0ms	10×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	31
3	31
2	29
1	24
0	12

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

11.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
8.0ms	(+ (hypot re im) re)

series402.0ms

Counts

2 → 6

Calls

2 calls:

286.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
115.0ms	(+ (hypot re im) re)

simplify3.0s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
4	4675
3	1358
2	468
1	174
0	75

prune207.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
17.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1`
2×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 23

Calls

2 calls:

3.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series532.0ms

Counts

2 → 6

Calls

2 calls:

320.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
211.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify3.8s

Counts

29 → 29

Iterations

Iter	Nodes
done	5019
4	3291
3	1078
2	333
1	130
0	61

prune208.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
0.4b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
17.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
17.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
24×	`add-sqr-sqrt`
19×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`sqrt-pow1`
9×	`pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `pow-prod-down` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

22.0ms	(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
15.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series960.0ms

Counts

4 → 12

Calls

4 calls:

373.0ms	(sqrt (* (* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re))) 2.0))
183.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
180.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
224.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
3	1394
2	470
1	231
0	104

prune621.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
0.4b	(* (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))
17.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
17.4b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-pow1`
65×	`pow1`
31×	`sqrt-prod`
26×	`add-sqr-sqrt`
23×	`pow-prod-down`
20×	`pow1/2`
14×	`pow-prod-up`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`swap-sqr`
8×	`pow-sqr`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 112

Calls

4 calls:

6.0ms	(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
56.0ms	(* (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))
0.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series1.1s

Counts

4 → 12

Calls

4 calls:

366.0ms	(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0)))
333.0ms	(* (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))) (sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))))
230.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
213.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify2.5s

Counts

124 → 124

Iterations

Iter	Nodes
done	5005
3	3680
2	1121
1	405
0	169

prune609.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.2b

regimes309.0ms

Accuracy

0% (0.2b remaining)

Error of 13.6b against oracle of 13.4b and baseline of 13.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample2.0s

Algorithm

intervals

Results

527.0ms	5999×	body	80	valid
449.0ms	308×	body	640	valid
360.0ms	693×	body	2560	valid
251.0ms	488×	body	1280	valid
138.0ms	302×	body	5120	valid
25.0ms	145×	body	320	valid
8.0ms	65×	body	160	valid