Details

sample204.0ms

Algorithm

intervals

Results

29.0ms	192×	body	80	valid
26.0ms	26×	body	2560	valid
13.0ms	12×	body	5120	valid
9.0ms	13×	body	1280	valid
4.0ms	7×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	2×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	44
5	44
4	42
3	35
2	27
1	19
0	12

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- (hypot re im) re) 2.0)
0.1b	(sqrt (* (- (hypot re im) re) 2.0))
0.5b	(- (hypot re im) re)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
8×	`pow1`
5×	`add-cbrt-cube` `associate-l` `add-exp-log` `add-log-exp`
4×	`associate-*l/`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-r` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`sqrt-pow1` `sqrt-div` `pow-prod-down` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow1/2` `diff-log` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `unswap-sqr`

Counts

3 → 70

Calls

3 calls:

32.0ms	(* (- (hypot re im) re) 2.0)
10.0ms	(sqrt (* (- (hypot re im) re) 2.0))
13.0ms	(- (hypot re im) re)

series429.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(* (- (hypot re im) re) 2.0)
242.0ms	(sqrt (* (- (hypot re im) re) 2.0))
97.0ms	(- (hypot re im) re)

simplify3.9s

Counts

79 → 79

Iterations

Iter	Nodes
4	6201
3	1928
2	680
1	288
0	137

prune565.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.7b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
0.1b	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
15.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
7×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow-prod-down`
1×	`pow1/2` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 46

Calls

3 calls:

6.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
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))

series709.0ms

Counts

3 → 9

Calls

3 calls:

231.0ms	(* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)
286.0ms	(sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0))
192.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify729.0ms

Counts

55 → 55

Iterations

Iter	Nodes
3	2184
2	577
1	204
0	94

prune412.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (hypot re im) re)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`cbrt-prod` `prod-diff`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 71

Calls

4 calls:

11.0ms	(- (hypot re im) re)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
2.0ms	(cbrt 2.0)

series110.0ms

Counts

4 → 6

Calls

4 calls:

110.0ms	(- (hypot re im) re)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify1.1s

Counts

77 → 77

Iterations

Iter	Nodes
4	2404
3	816
2	278
1	145
0	84

prune733.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.7b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
0.5b	(* (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))))
15.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
15.5b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite57.0ms

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` `insert-posit16` `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 → 116

Calls

4 calls:

4.0ms	(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
51.0ms	(* (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))

series1.2s

Counts

4 → 12

Calls

4 calls:

424.0ms	(sqrt (sqrt (* (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)) 2.0)))
364.0ms	(* (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))))
210.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
226.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify1.4s

Counts

128 → 128

Iterations

Iter	Nodes
3	3733
2	1153
1	418
0	177

prune943.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.6b

regimes487.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.7b and baseline of 12.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	11
1	11
0	9

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.2s	6071×	body	80	valid
541.0ms	712×	body	2560	valid
291.0ms	441×	body	1280	valid
288.0ms	299×	body	5120	valid
120.0ms	268×	body	640	valid
45.0ms	141×	body	320	valid
17.0ms	68×	body	160	valid