Details

sample95.0ms

Algorithm

intervals

Results

29.0ms	196×	body	80	valid
19.0ms	21×	body	2560	valid
11.0ms	10×	body	5120	valid
11.0ms	14×	body	1280	valid
7.0ms	11×	body	640	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* (+ (hypot re im) re) 2.0))
0.6b	(+ (hypot re im) re)

rewrite22.0ms

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:

12.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
9.0ms	(+ (hypot re im) re)

series348.0ms

Counts

2 → 6

Calls

2 calls:

259.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
89.0ms	(+ (hypot re im) re)

simplify2.6s

Counts

40 → 40

Iterations

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

prune375.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.9b

localize34.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
0.6b	(+ (hypot re im) re)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `sqrt-prod`
7×	`associate-l` `add-cube-cbrt`
6×	`pow1` `associate-r`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp` `unswap-sqr`
3×	`fma-def` `pow-prod-down`
2×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `associate-*l/` `flip-+` `insert-posit16` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

2 → 54

Calls

2 calls:

17.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
7.0ms	(+ (hypot re im) re)

series337.0ms

Counts

2 → 6

Calls

2 calls:

259.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
79.0ms	(+ (hypot re im) re)

simplify4.8s

Counts

60 → 60

Iterations

Iter	Nodes
4	4788
3	1694
2	645
1	235
0	101

prune630.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize44.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.2b	(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
0.6b	(+ (hypot re im) re)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

31×	`sqrt-prod`
24×	`add-sqr-sqrt`
18×	`associate-r`
16×	`*-un-lft-identity`
15×	`pow1`
12×	`add-cube-cbrt`
10×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
8×	`associate-l`
6×	`associate-*l/` `unswap-sqr`
5×	`sqrt-pow1` `pow1/2` `add-log-exp`
4×	`sqrt-div` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-unprod` `flip-+` `insert-posit16` `log1p-expm1-u`
2×	`*-commutative` `distribute-lft-out`
1×	`+-commutative` `sum-log`

Counts

3 → 91

Calls

3 calls:

55.0ms	(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
37.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
9.0ms	(+ (hypot re im) re)

series705.0ms

Counts

3 → 9

Calls

3 calls:

280.0ms	(* (* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
336.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt (sqrt 2.0)))
89.0ms	(+ (hypot re im) re)

simplify2.0s

Counts

100 → 100

Iterations

Iter	Nodes
3	3885
2	1145
1	387
0	149

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
14.7b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite9.0ms

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:

8.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series572.0ms

Counts

2 → 6

Calls

2 calls:

371.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re) 2.0))
200.0ms	(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

prune324.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.9b

regimes530.0ms

Accuracy

0% (0.3b remaining)

Error of 13.7b against oracle of 13.4b and baseline of 13.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

920.0ms	5993×	body	80	valid
896.0ms	700×	body	2560	valid
296.0ms	491×	body	1280	valid
257.0ms	271×	body	5120	valid
167.0ms	319×	body	640	valid
51.0ms	160×	body	320	valid
14.0ms	66×	body	160	valid