Details

sample122.0ms

Algorithm

intervals

Results

29.0ms	190×	body	80	valid
28.0ms	15×	body	1280	valid
25.0ms	25×	body	2560	valid
14.0ms	12×	body	5120	valid
5.0ms	8×	body	640	valid
2.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	31
3	31
2	29
1	24
0	12

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (+ (hypot re im) re) 2.0))
0.3b	(+ (hypot re im) re)

rewrite24.0ms

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-+` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

2 → 34

Calls

2 calls:

18.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
6.0ms	(+ (hypot re im) re)

series382.0ms

Counts

2 → 6

Calls

2 calls:

285.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
96.0ms	(+ (hypot re im) re)

simplify2.4s

Counts

40 → 40

Iterations

Iter	Nodes
4	3960
3	1293
2	458
1	175
0	77

prune239.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
16.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite5.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow1/2` `pow-prod-down` `sqrt-prod` `fma-udef`

Counts

2 → 25

Calls

2 calls:

4.0ms	(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)

series517.0ms

Counts

2 → 6

Calls

2 calls:

334.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
183.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify1.9s

Counts

31 → 31

Iterations

Iter	Nodes
4	3033
3	1011
2	329
1	130
0	63

prune170.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.6b

localize26.0ms

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)))
16.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
16.2b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite44.0ms

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` `insert-posit16` `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 → 89

Calls

4 calls:

29.0ms	(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))
13.0ms	(* (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)

series876.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(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))
188.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
176.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)
189.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify3.4s

Counts

101 → 101

Iterations

Iter	Nodes
4	5101
3	1470
2	524
1	224
0	107

prune502.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.6b

localize37.0ms

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)) (cbrt (hypot re im)))
16.1b	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 82

Calls

4 calls:

1.0ms	(cbrt (hypot re im))
1.0ms	(cbrt (hypot re im))
8.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
0.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

series680.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt (hypot re im))
162.0ms	(cbrt (hypot re im))
159.0ms	(* (cbrt (hypot re im)) (cbrt (hypot re im)))
187.0ms	(fma (* (cbrt (hypot re im)) (cbrt (hypot re im))) (cbrt (hypot re im)) re)

simplify1.3s

Counts

94 → 94

Iterations

Iter	Nodes
4	2856
3	1012
2	415
1	183
0	94

prune494.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 12.6b

regimes241.0ms

Accuracy

0% (0.3b remaining)

Error of 13.6b against oracle of 13.3b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

901.0ms	703×	body	2560	valid
844.0ms	5970×	body	80	valid
388.0ms	481×	body	1280	valid
250.0ms	307×	body	5120	valid
149.0ms	289×	body	640	valid
54.0ms	167×	body	320	valid
17.0ms	83×	body	160	valid